TSTP Solution File: BOO004-10 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : BOO004-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n022.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 : Thu Jul 14 23:47:57 EDT 2022

% Result   : Unsatisfiable 4.11s 4.44s
% Output   : Refutation 4.11s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : BOO004-10 : TPTP v8.1.0. Released v7.5.0.
% 0.12/0.14  % Command  : tptp2X_and_run_prover9 %d %s
% 0.14/0.35  % Computer : n022.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % 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 : Wed Jun  1 23:22:22 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 4.11/4.44  ============================== Prover9 ===============================
% 4.11/4.44  Prover9 (32) version 2009-11A, November 2009.
% 4.11/4.44  Process 27439 was started by sandbox2 on n022.cluster.edu,
% 4.11/4.44  Wed Jun  1 23:22:22 2022
% 4.11/4.44  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27286_n022.cluster.edu".
% 4.11/4.44  ============================== end of head ===========================
% 4.11/4.44  
% 4.11/4.44  ============================== INPUT =================================
% 4.11/4.44  
% 4.11/4.44  % Reading from file /tmp/Prover9_27286_n022.cluster.edu
% 4.11/4.44  
% 4.11/4.44  set(prolog_style_variables).
% 4.11/4.44  set(auto2).
% 4.11/4.44      % set(auto2) -> set(auto).
% 4.11/4.44      % set(auto) -> set(auto_inference).
% 4.11/4.44      % set(auto) -> set(auto_setup).
% 4.11/4.44      % set(auto_setup) -> set(predicate_elim).
% 4.11/4.44      % set(auto_setup) -> assign(eq_defs, unfold).
% 4.11/4.44      % set(auto) -> set(auto_limits).
% 4.11/4.44      % set(auto_limits) -> assign(max_weight, "100.000").
% 4.11/4.44      % set(auto_limits) -> assign(sos_limit, 20000).
% 4.11/4.44      % set(auto) -> set(auto_denials).
% 4.11/4.44      % set(auto) -> set(auto_process).
% 4.11/4.44      % set(auto2) -> assign(new_constants, 1).
% 4.11/4.44      % set(auto2) -> assign(fold_denial_max, 3).
% 4.11/4.44      % set(auto2) -> assign(max_weight, "200.000").
% 4.11/4.44      % set(auto2) -> assign(max_hours, 1).
% 4.11/4.44      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.11/4.44      % set(auto2) -> assign(max_seconds, 0).
% 4.11/4.44      % set(auto2) -> assign(max_minutes, 5).
% 4.11/4.44      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.11/4.44      % set(auto2) -> set(sort_initial_sos).
% 4.11/4.44      % set(auto2) -> assign(sos_limit, -1).
% 4.11/4.44      % set(auto2) -> assign(lrs_ticks, 3000).
% 4.11/4.44      % set(auto2) -> assign(max_megs, 400).
% 4.11/4.44      % set(auto2) -> assign(stats, some).
% 4.11/4.44      % set(auto2) -> clear(echo_input).
% 4.11/4.44      % set(auto2) -> set(quiet).
% 4.11/4.44      % set(auto2) -> clear(print_initial_clauses).
% 4.11/4.44      % set(auto2) -> clear(print_given).
% 4.11/4.44  assign(lrs_ticks,-1).
% 4.11/4.44  assign(sos_limit,10000).
% 4.11/4.44  assign(order,kbo).
% 4.11/4.44  set(lex_order_vars).
% 4.11/4.44  clear(print_given).
% 4.11/4.44  
% 4.11/4.44  % formulas(sos).  % not echoed (25 formulas)
% 4.11/4.44  
% 4.11/4.44  ============================== end of input ==========================
% 4.11/4.44  
% 4.11/4.44  % From the command line: assign(max_seconds, 300).
% 4.11/4.44  
% 4.11/4.44  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.11/4.44  
% 4.11/4.44  % Formulas that are not ordinary clauses:
% 4.11/4.44  
% 4.11/4.44  ============================== end of process non-clausal formulas ===
% 4.11/4.44  
% 4.11/4.44  ============================== PROCESS INITIAL CLAUSES ===============
% 4.11/4.44  
% 4.11/4.44  ============================== PREDICATE ELIMINATION =================
% 4.11/4.44  
% 4.11/4.44  ============================== end predicate elimination =============
% 4.11/4.44  
% 4.11/4.44  Auto_denials:
% 4.11/4.44    % copying label prove_both_equalities to answer in negative clause
% 4.11/4.44  
% 4.11/4.44  Term ordering decisions:
% 4.11/4.44  
% 4.11/4.44  % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 4.11/4.44  Function symbol KB weights:  true=1. additive_identity=1. multiplicative_identity=1. x=1. add=1. multiply=1. product=1. sum=1. ifeq=1. ifeq2=1. inverse=0.
% 4.11/4.44  
% 4.11/4.44  ============================== end of process initial clauses ========
% 4.11/4.44  
% 4.11/4.44  ============================== CLAUSES FOR SEARCH ====================
% 4.11/4.44  
% 4.11/4.44  ============================== end of clauses for search =============
% 4.11/4.44  
% 4.11/4.44  ============================== SEARCH ================================
% 4.11/4.44  
% 4.11/4.44  % Starting search at 0.01 seconds.
% 4.11/4.44  
% 4.11/4.44  Low Water (keep): wt=36.000, iters=3352
% 4.11/4.44  
% 4.11/4.44  Low Water (keep): wt=34.000, iters=3337
% 4.11/4.44  
% 4.11/4.44  Low Water (keep): wt=33.000, iters=3427
% 4.11/4.44  
% 4.11/4.44  Low Water (keep): wt=32.000, iters=3406
% 4.11/4.44  
% 4.11/4.44  Low Water (keep): wt=31.000, iters=3356
% 4.11/4.44  
% 4.11/4.44  Low Water (keep): wt=30.000, iters=3358
% 4.11/4.44  
% 4.11/4.44  Low Water (keep): wt=29.000, iters=3365
% 4.11/4.44  
% 4.11/4.44  Low Water (keep): wt=28.000, iters=3335
% 4.11/4.44  
% 4.11/4.44  ============================== PROOF =================================
% 4.11/4.44  % SZS status Unsatisfiable
% 4.11/4.44  % SZS output start Refutation
% 4.11/4.44  
% 4.11/4.44  % Proof 1 at 3.40 (+ 0.05) seconds: prove_both_equalities.
% 4.11/4.44  % Length of proof is 80.
% 4.11/4.44  % Level of proof is 19.
% 4.11/4.44  % Maximum clause weight is 34.000.
% 4.11/4.44  % Given clauses 1174.
% 4.11/4.44  
% 4.11/4.44  1 sum(additive_identity,A,A) = true # label(additive_identity1) # label(axiom).  [assumption].
% 4.11/4.44  2 sum(A,additive_identity,A) = true # label(additive_identity2) # label(axiom).  [assumption].
% 4.11/4.44  3 product(multiplicative_identity,A,A) = true # label(multiplicative_identity1) # label(axiom).  [assumption].
% 4.11/4.44  4 product(A,multiplicative_identity,A) = true # label(multiplicative_identity2) # label(axiom).  [assumption].
% 4.11/4.44  5 ifeq2(A,A,B,C) = B # label(ifeq_axiom) # label(axiom).  [assumption].
% 4.11/4.44  6 ifeq(A,A,B,C) = B # label(ifeq_axiom_001) # label(axiom).  [assumption].
% 4.11/4.44  10 product(A,inverse(A),additive_identity) = true # label(multiplicative_inverse2) # label(axiom).  [assumption].
% 4.11/4.44  11 sum(A,B,add(A,B)) = true # label(closure_of_addition) # label(axiom).  [assumption].
% 4.11/4.44  12 product(A,B,multiply(A,B)) = true # label(closure_of_multiplication) # label(axiom).  [assumption].
% 4.11/4.44  13 ifeq(sum(A,B,C),true,sum(B,A,C),true) = true # label(commutativity_of_addition) # label(axiom).  [assumption].
% 4.11/4.44  14 ifeq(product(A,B,C),true,product(B,A,C),true) = true # label(commutativity_of_multiplication) # label(axiom).  [assumption].
% 4.11/4.44  15 ifeq2(sum(A,B,C),true,ifeq2(sum(A,B,D),true,D,C),C) = C # label(addition_is_well_defined) # label(axiom).  [assumption].
% 4.11/4.44  16 ifeq2(product(A,B,C),true,ifeq2(product(A,B,D),true,D,C),C) = C # label(multiplication_is_well_defined) # label(axiom).  [assumption].
% 4.11/4.44  17 ifeq(product(A,B,C),true,ifeq(product(A,D,E),true,ifeq(product(A,F,V6),true,ifeq(sum(F,D,B),true,sum(V6,E,C),true),true),true),true) = true # label(distributivity1) # label(axiom).  [assumption].
% 4.11/4.44  23 ifeq(product(A,B,C),true,ifeq(sum(C,D,E),true,ifeq(sum(B,D,F),true,ifeq(sum(A,D,V6),true,product(V6,F,E),true),true),true),true) = true # label(distributivity7) # label(axiom).  [assumption].
% 4.11/4.44  25 sum(x,x,x) != true # label(prove_both_equalities) # label(negated_conjecture) # answer(prove_both_equalities).  [assumption].
% 4.11/4.44  26 sum(A,B,add(B,A)) = true.  [para(11(a,1),13(a,1,1)),rewrite([6(6)])].
% 4.11/4.44  27 product(A,B,multiply(B,A)) = true.  [para(12(a,1),14(a,1,1)),rewrite([6(6)])].
% 4.11/4.44  28 ifeq2(sum(additive_identity,A,B),true,B,A) = A.  [para(1(a,1),15(a,1,1)),rewrite([5(7)])].
% 4.11/4.44  30 ifeq2(sum(A,additive_identity,B),true,B,A) = A.  [para(2(a,1),15(a,1,1)),rewrite([5(7)])].
% 4.11/4.44  36 ifeq2(sum(A,B,C),true,C,add(A,B)) = add(A,B).  [para(11(a,1),15(a,1,1)),rewrite([5(8)])].
% 4.11/4.44  37 ifeq2(sum(A,B,C),true,add(A,B),C) = C.  [para(11(a,1),15(a,1,3,1)),rewrite([5(6)])].
% 4.11/4.44  38 ifeq2(product(multiplicative_identity,A,B),true,B,A) = A.  [para(3(a,1),16(a,1,1)),rewrite([5(7)])].
% 4.11/4.44  40 ifeq2(product(A,multiplicative_identity,B),true,B,A) = A.  [para(4(a,1),16(a,1,1)),rewrite([5(7)])].
% 4.11/4.44  47 ifeq2(product(A,B,C),true,multiply(A,B),C) = C.  [para(12(a,1),16(a,1,3,1)),rewrite([5(6)])].
% 4.11/4.44  48 ifeq(product(A,B,C),true,ifeq(product(A,B,D),true,ifeq(product(A,additive_identity,E),true,sum(E,D,C),true),true),true) = true.  [para(1(a,1),17(a,1,3,3,3,1)),rewrite([6(12)])].
% 4.11/4.44  52 ifeq(product(multiplicative_identity,A,B),true,ifeq(product(multiplicative_identity,C,D),true,ifeq(sum(C,A,E),true,sum(D,B,E),true),true),true) = true.  [para(3(a,1),17(a,1,1)),rewrite([6(19)])].
% 4.11/4.44  53 ifeq(product(multiplicative_identity,A,B),true,ifeq(product(multiplicative_identity,C,D),true,ifeq(sum(C,E,A),true,sum(D,E,B),true),true),true) = true.  [para(3(a,1),17(a,1,3,1)),rewrite([6(17)])].
% 4.11/4.44  56 ifeq(product(A,B,C),true,ifeq(product(A,D,E),true,ifeq(sum(D,multiplicative_identity,B),true,sum(E,A,C),true),true),true) = true.  [para(4(a,1),17(a,1,3,1)),rewrite([6(16)])].
% 4.11/4.44  201 ifeq(product(A,B,additive_identity),true,ifeq(sum(B,C,D),true,ifeq(sum(A,C,E),true,product(E,D,C),true),true),true) = true.  [para(1(a,1),23(a,1,3,1)),rewrite([6(16)])].
% 4.11/4.44  298 add(A,additive_identity) = A.  [para(26(a,1),28(a,1,1)),rewrite([5(5)])].
% 4.11/4.44  301 multiply(A,multiplicative_identity) = A.  [para(27(a,1),38(a,1,1)),rewrite([5(5)])].
% 4.11/4.44  306 add(A,B) = add(B,A).  [para(26(a,1),36(a,1,1)),rewrite([5(5)])].
% 4.11/4.44  307 multiply(A,B) = multiply(B,A).  [para(27(a,1),47(a,1,1)),rewrite([5(5)])].
% 4.11/4.44  315 ifeq(product(multiplicative_identity,A,B),true,ifeq(product(multiplicative_identity,additive_identity,C),true,sum(C,B,A),true),true) = true.  [para(3(a,1),48(a,1,1)),rewrite([6(16)])].
% 4.11/4.44  324 ifeq(product(A,inverse(A),B),true,ifeq(product(A,additive_identity,C),true,sum(C,B,additive_identity),true),true) = true.  [para(10(a,1),48(a,1,1)),rewrite([6(16)])].
% 4.11/4.44  349 ifeq(product(multiplicative_identity,A,B),true,sum(additive_identity,B,A),true) = true.  [para(3(a,1),315(a,1,3,1)),rewrite([6(9)])].
% 4.11/4.44  388 ifeq(product(multiplicative_identity,A,B),true,ifeq(sum(A,C,D),true,sum(B,C,D),true),true) = true.  [para(3(a,1),52(a,1,1)),rewrite([6(14)])].
% 4.11/4.44  402 ifeq(product(multiplicative_identity,A,B),true,ifeq(sum(C,D,A),true,sum(C,D,B),true),true) = true.  [para(3(a,1),53(a,1,3,1)),rewrite([6(12)])].
% 4.11/4.44  529 ifeq(product(A,B,C),true,ifeq(sum(multiplicative_identity,multiplicative_identity,B),true,sum(A,A,C),true),true) = true.  [para(4(a,1),56(a,1,3,1)),rewrite([6(13)])].
% 4.11/4.44  1471 ifeq(product(multiplicative_identity,A,B),true,sum(B,C,add(A,C)),true) = true.  [para(11(a,1),388(a,1,3,1)),rewrite([6(9)])].
% 4.11/4.44  5299 ifeq(product(A,additive_identity,additive_identity),true,ifeq(sum(A,B,C),true,product(C,B,B),true),true) = true.  [para(1(a,1),201(a,1,3,1)),rewrite([6(13)])].
% 4.11/4.44  5444 ifeq(product(multiplicative_identity,add(A,B),C),true,sum(A,B,C),true) = true.  [para(11(a,1),402(a,1,3,1)),rewrite([6(9)])].
% 4.11/4.44  5484 sum(A,B,multiply(multiplicative_identity,add(A,B))) = true.  [para(12(a,1),5444(a,1,1)),rewrite([6(8)])].
% 4.11/4.44  5508 multiply(multiplicative_identity,add(A,B)) = add(A,B).  [para(5484(a,1),36(a,1,1)),rewrite([5(7)])].
% 4.11/4.44  6629 ifeq(product(A,add(multiplicative_identity,multiplicative_identity),B),true,sum(A,A,B),true) = true.  [para(11(a,1),529(a,1,3,1)),rewrite([6(10)])].
% 4.11/4.44  6973 sum(A,A,multiply(A,add(multiplicative_identity,multiplicative_identity))) = true.  [para(12(a,1),6629(a,1,1)),rewrite([6(9)])].
% 4.11/4.44  6975 ifeq2(sum(A,A,B),true,multiply(A,add(multiplicative_identity,multiplicative_identity)),B) = B.  [para(6973(a,1),15(a,1,3,1)),rewrite([5(9)])].
% 4.11/4.44  6997 multiply(A,add(multiplicative_identity,multiplicative_identity)) = add(A,A).  [para(6973(a,1),36(a,1,1)),rewrite([5(8)])].
% 4.11/4.44  7479 multiply(multiplicative_identity,multiply(A,add(multiplicative_identity,multiplicative_identity))) = add(A,A).  [para(6997(a,2),5508(a,1,2))].
% 4.11/4.44  7966 product(multiplicative_identity,multiply(A,add(multiplicative_identity,multiplicative_identity)),add(A,A)) = true.  [para(7479(a,1),12(a,1,3))].
% 4.11/4.44  8450 sum(additive_identity,add(A,A),multiply(A,add(multiplicative_identity,multiplicative_identity))) = true.  [para(7966(a,1),349(a,1,1)),rewrite([6(11)])].
% 4.11/4.44  8509 sum(add(A,A),B,add(B,multiply(A,add(multiplicative_identity,multiplicative_identity)))) = true.  [para(7966(a,1),1471(a,1,1)),rewrite([306(8),6(11)])].
% 4.11/4.44  8827 multiply(A,add(multiplicative_identity,multiplicative_identity)) = add(additive_identity,add(A,A)).  [para(8450(a,1),36(a,1,1)),rewrite([5(10)])].
% 4.11/4.44  8953 add(additive_identity,add(A,A)) = add(A,A).  [para(8827(a,1),6997(a,1))].
% 4.11/4.44  9531 add(A,multiply(B,add(multiplicative_identity,multiplicative_identity))) = add(A,add(B,B)).  [para(8509(a,1),36(a,1,1)),rewrite([306(9),5(10),306(7)])].
% 4.11/4.44  9603 sum(multiply(A,add(multiplicative_identity,multiplicative_identity)),B,add(B,multiply(A,add(multiplicative_identity,multiplicative_identity)))) = true.  [para(6997(a,2),8509(a,1,1))].
% 4.11/4.44  9611 add(add(A,A),multiply(A,add(multiplicative_identity,multiplicative_identity))) = multiply(add(A,A),add(multiplicative_identity,multiplicative_identity)).  [para(8509(a,1),6975(a,1,1)),rewrite([5(14)]),flip(a)].
% 4.11/4.44  9743 sum(A,multiply(B,add(multiplicative_identity,multiplicative_identity)),add(A,add(B,B))) = true.  [para(9531(a,1),11(a,1,3))].
% 4.11/4.44  9747 ifeq2(sum(A,add(B,B),C),true,add(A,multiply(B,add(multiplicative_identity,multiplicative_identity))),C) = C.  [para(9531(a,2),37(a,1,3))].
% 4.11/4.44  10520 add(multiply(A,add(multiplicative_identity,multiplicative_identity)),multiply(A,add(multiplicative_identity,multiplicative_identity))) = multiply(add(multiplicative_identity,multiplicative_identity),multiply(A,add(multiplicative_identity,multiplicative_identity))).  [para(9603(a,1),6975(a,1,1)),rewrite([307(10),5(20)]),flip(a)].
% 4.11/4.44  10836 multiply(add(multiplicative_identity,multiplicative_identity),multiply(A,add(multiplicative_identity,multiplicative_identity))) = multiply(add(A,A),add(multiplicative_identity,multiplicative_identity)).  [para(6997(a,2),9611(a,1,1)),rewrite([10520(9)])].
% 4.11/4.44  11031 multiply(add(multiplicative_identity,multiplicative_identity),multiply(A,add(multiplicative_identity,multiplicative_identity))) = add(add(A,A),add(A,A)).  [para(10836(a,2),6997(a,1))].
% 4.11/4.44  11155 multiply(add(multiplicative_identity,multiplicative_identity),add(A,A)) = add(add(A,A),add(A,A)).  [para(6997(a,1),11031(a,1,2))].
% 4.11/4.44  11197 add(add(A,A),add(A,A)) = add(additive_identity,multiply(add(multiplicative_identity,multiplicative_identity),add(A,A))).  [para(11155(a,2),8953(a,1,2)),flip(a)].
% 4.11/4.44  11219 sum(add(A,A),multiply(A,add(multiplicative_identity,multiplicative_identity)),multiply(add(multiplicative_identity,multiplicative_identity),add(A,A))) = true.  [para(11155(a,2),9743(a,1,3))].
% 4.11/4.44  11349 add(additive_identity,multiply(add(multiplicative_identity,multiplicative_identity),add(A,A))) = multiply(add(A,A),add(multiplicative_identity,multiplicative_identity)).  [para(11197(a,1),6997(a,2)),flip(a)].
% 4.11/4.44  11363 multiply(add(multiplicative_identity,multiplicative_identity),add(add(A,A),add(A,A))) = add(additive_identity,multiply(add(multiplicative_identity,multiplicative_identity),multiply(add(multiplicative_identity,multiplicative_identity),multiply(A,add(multiplicative_identity,multiplicative_identity))))).  [para(11031(a,2),11349(a,1,2,2)),rewrite([307(21)]),flip(a)].
% 4.11/4.44  11559 add(multiply(A,add(multiplicative_identity,multiplicative_identity)),multiply(B,add(multiplicative_identity,multiplicative_identity))) = add(add(B,B),multiply(A,add(multiplicative_identity,multiplicative_identity))).  [para(9603(a,1),9747(a,1,1)),rewrite([5(18)])].
% 4.11/4.44  11930 ifeq(product(A,additive_identity,B),true,sum(B,additive_identity,additive_identity),true) = true.  [para(10(a,1),324(a,1,1)),rewrite([6(12)])].
% 4.11/4.44  11998 sum(multiply(A,additive_identity),additive_identity,additive_identity) = true.  [para(12(a,1),11930(a,1,1)),rewrite([6(9)])].
% 4.11/4.44  12002 multiply(A,additive_identity) = additive_identity.  [para(11998(a,1),30(a,1,1)),rewrite([5(6)]),flip(a)].
% 4.11/4.44  12110 product(A,additive_identity,additive_identity) = true.  [para(12002(a,1),12(a,1,3))].
% 4.11/4.44  12138 ifeq(sum(A,B,C),true,product(C,B,B),true) = true.  [back_rewrite(5299),rewrite([12110(3),6(9)])].
% 4.11/4.44  12340 product(add(A,B),B,B) = true.  [para(11(a,1),12138(a,1,1)),rewrite([6(6)])].
% 4.11/4.44  12539 add(A,multiplicative_identity) = multiplicative_identity.  [para(12340(a,1),40(a,1,1)),rewrite([5(6)]),flip(a)].
% 4.11/4.44  12790 add(A,add(B,B)) = add(A,B).  [back_rewrite(11559),rewrite([12539(3),301(2),12539(3),301(2),12539(5),301(4),306(3)]),flip(a)].
% 4.11/4.44  12820 add(A,A) = A.  [back_rewrite(11363),rewrite([12539(3),12790(4),306(3),12790(3),5508(3),12539(5),12539(6),12539(7),301(6),307(5),301(5),307(4),301(4),306(3),298(3)])].
% 4.11/4.44  12823 sum(A,A,A) = true.  [back_rewrite(11219),rewrite([12820(1),12820(3),301(2),12820(3),12820(2),307(2),301(2)])].
% 4.11/4.44  12824 $F # answer(prove_both_equalities).  [resolve(12823,a,25,a)].
% 4.11/4.44  
% 4.11/4.44  % SZS output end Refutation
% 4.11/4.44  ============================== end of proof ==========================
% 4.11/4.44  
% 4.11/4.44  ============================== STATISTICS ============================
% 4.11/4.44  
% 4.11/4.44  Given=1174. Generated=68336. Kept=12823. proofs=1.
% 4.11/4.44  Usable=456. Sos=4448. Demods=5144. Limbo=284, Disabled=7659. Hints=0.
% 4.11/4.44  Megabytes=16.00.
% 4.11/4.44  User_CPU=3.40, System_CPU=0.05, Wall_clock=4.
% 4.11/4.44  
% 4.11/4.44  ============================== end of statistics =====================
% 4.11/4.44  
% 4.11/4.44  ============================== end of search =========================
% 4.11/4.44  
% 4.11/4.44  THEOREM PROVED
% 4.11/4.44  % SZS status Unsatisfiable
% 4.11/4.44  
% 4.11/4.44  Exiting with 1 proof.
% 4.11/4.44  
% 4.11/4.44  Process 27439 exit (max_proofs) Wed Jun  1 23:22:26 2022
% 4.11/4.44  Prover9 interrupted
%------------------------------------------------------------------------------