TSTP Solution File: GRP175-4 by EQP---0.9e

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : EQP---0.9e
% Problem  : GRP175-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_eqp %s

% Computer : n019.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 08:45:43 EDT 2022

% Result   : Unsatisfiable 4.16s 4.61s
% Output   : Refutation 4.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   43 (  43 unt;   0 nHn;   4 RR)
%            Number of literals    :   43 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   80 (   9 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,plain,
    equal(multiply(identity,A),A),
    file('GRP175-4.p',unknown),
    [] ).

cnf(2,plain,
    equal(multiply(inverse(A),A),identity),
    file('GRP175-4.p',unknown),
    [] ).

cnf(3,plain,
    equal(multiply(multiply(A,B),C),multiply(A,multiply(B,C))),
    file('GRP175-4.p',unknown),
    [] ).

cnf(4,plain,
    equal(greatest_lower_bound(A,B),greatest_lower_bound(B,A)),
    file('GRP175-4.p',unknown),
    [] ).

cnf(5,plain,
    equal(least_upper_bound(A,B),least_upper_bound(B,A)),
    file('GRP175-4.p',unknown),
    [] ).

cnf(7,plain,
    equal(least_upper_bound(least_upper_bound(A,B),C),least_upper_bound(A,least_upper_bound(B,C))),
    inference(flip,[status(thm),theory(equality)],[1]),
    [iquote('flip(1)')] ).

cnf(8,plain,
    equal(least_upper_bound(A,A),A),
    file('GRP175-4.p',unknown),
    [] ).

cnf(10,plain,
    equal(least_upper_bound(A,greatest_lower_bound(A,B)),A),
    file('GRP175-4.p',unknown),
    [] ).

cnf(12,plain,
    equal(multiply(A,least_upper_bound(B,C)),least_upper_bound(multiply(A,B),multiply(A,C))),
    file('GRP175-4.p',unknown),
    [] ).

cnf(14,plain,
    equal(multiply(least_upper_bound(A,B),C),least_upper_bound(multiply(A,C),multiply(B,C))),
    file('GRP175-4.p',unknown),
    [] ).

cnf(15,plain,
    equal(multiply(greatest_lower_bound(A,B),C),greatest_lower_bound(multiply(A,C),multiply(B,C))),
    file('GRP175-4.p',unknown),
    [] ).

cnf(16,plain,
    equal(greatest_lower_bound(identity,b),identity),
    file('GRP175-4.p',unknown),
    [] ).

cnf(17,plain,
    ~ equal(least_upper_bound(identity,multiply(inverse(a),multiply(b,a))),multiply(inverse(a),multiply(b,a))),
    file('GRP175-4.p',unknown),
    [] ).

cnf(18,plain,
    equal(multiply(inverse(A),multiply(A,B)),B),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[2,3]),1]),1]),
    [iquote('para(2,3),demod([1]),flip(1)')] ).

cnf(25,plain,
    equal(multiply(inverse(identity),A),A),
    inference(para,[status(thm),theory(equality)],[1,18]),
    [iquote('para(1,18)')] ).

cnf(26,plain,
    equal(least_upper_bound(A,greatest_lower_bound(B,A)),A),
    inference(para,[status(thm),theory(equality)],[4,10]),
    [iquote('para(4,10)')] ).

cnf(29,plain,
    equal(least_upper_bound(A,least_upper_bound(B,C)),least_upper_bound(B,least_upper_bound(A,C))),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[5,7]),7]),
    [iquote('para(5,7),demod([7])')] ).

cnf(32,plain,
    equal(least_upper_bound(A,least_upper_bound(A,B)),least_upper_bound(A,B)),
    inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[8,7]),1]),
    [iquote('para(8,7),flip(1)')] ).

cnf(48,plain,
    equal(multiply(inverse(inverse(A)),identity),A),
    inference(para,[status(thm),theory(equality)],[2,18]),
    [iquote('para(2,18)')] ).

cnf(50,plain,
    equal(multiply(inverse(inverse(identity)),A),A),
    inference(para,[status(thm),theory(equality)],[25,18]),
    [iquote('para(25,18)')] ).

cnf(51,plain,
    equal(inverse(identity),identity),
    inference(para,[status(thm),theory(equality)],[50,2]),
    [iquote('para(50,2)')] ).

cnf(54,plain,
    equal(multiply(inverse(inverse(A)),B),multiply(A,B)),
    inference(para,[status(thm),theory(equality)],[18,18]),
    [iquote('para(18,18)')] ).

cnf(55,plain,
    equal(multiply(A,identity),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[48]),54]),
    [iquote('back_demod(48),demod([54])')] ).

cnf(57,plain,
    equal(inverse(inverse(A)),A),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[54,55]),55]),1]),
    [iquote('para(54,55),demod([55]),flip(1)')] ).

cnf(58,plain,
    equal(multiply(A,inverse(A)),identity),
    inference(para,[status(thm),theory(equality)],[57,2]),
    [iquote('para(57,2)')] ).

cnf(61,plain,
    equal(greatest_lower_bound(A,multiply(b,A)),A),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[16,15]),1,1]),1]),
    [iquote('para(16,15),demod([1,1]),flip(1)')] ).

cnf(66,plain,
    equal(multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))),C),
    inference(para,[status(thm),theory(equality)],[3,18]),
    [iquote('para(3,18)')] ).

cnf(67,plain,
    equal(least_upper_bound(multiply(b,A),A),multiply(b,A)),
    inference(para,[status(thm),theory(equality)],[61,26]),
    [iquote('para(61,26)')] ).

cnf(68,plain,
    equal(least_upper_bound(multiply(inverse(least_upper_bound(A,B)),multiply(A,C)),multiply(inverse(least_upper_bound(A,B)),multiply(B,C))),C),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[14,18]),12]),
    [iquote('para(14,18),demod([12])')] ).

cnf(144,plain,
    equal(least_upper_bound(A,least_upper_bound(B,least_upper_bound(A,C))),least_upper_bound(B,least_upper_bound(A,C))),
    inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[32,29]),1]),
    [iquote('para(32,29),flip(1)')] ).

cnf(352,plain,
    equal(multiply(A,multiply(inverse(A),B)),B),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[58,3]),1]),1]),
    [iquote('para(58,3),demod([1]),flip(1)')] ).

cnf(427,plain,
    equal(inverse(multiply(inverse(multiply(A,B)),A)),B),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[2,66]),55]),
    [iquote('para(2,66),demod([55])')] ).

cnf(438,plain,
    equal(inverse(multiply(inverse(A),B)),multiply(inverse(B),A)),
    inference(para,[status(thm),theory(equality)],[352,427]),
    [iquote('para(352,427)')] ).

cnf(439,plain,
    equal(inverse(multiply(A,B)),multiply(inverse(B),inverse(A))),
    inference(para,[status(thm),theory(equality)],[57,438]),
    [iquote('para(57,438)')] ).

cnf(456,plain,
    equal(least_upper_bound(multiply(inverse(least_upper_bound(A,least_upper_bound(B,C))),multiply(A,D)),least_upper_bound(multiply(inverse(least_upper_bound(A,least_upper_bound(B,C))),multiply(B,D)),multiply(inverse(least_upper_bound(A,least_upper_bound(B,C))),multiply(C,D)))),D),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[7,68]),14,12,7,7]),
    [iquote('para(7,68),demod([14,12,7,7])')] ).

cnf(483,plain,
    equal(least_upper_bound(A,multiply(inverse(B),multiply(inverse(b),multiply(B,A)))),A),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[67,68]),439,3,3,18,18,67,439,3]),
    [iquote('para(67,68),demod([439,3,3,18,18,67,439,3])')] ).

cnf(1673,plain,
    equal(least_upper_bound(identity,multiply(inverse(A),multiply(inverse(b),A))),identity),
    inference(para,[status(thm),theory(equality)],[55,483]),
    [iquote('para(55,483)')] ).

cnf(1972,plain,
    equal(least_upper_bound(multiply(inverse(least_upper_bound(A,least_upper_bound(B,C))),multiply(B,D)),D),D),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[144,68]),144,14,14,12,12,456]),
    [iquote('para(144,68),demod([144,14,14,12,12,456])')] ).

cnf(7935,plain,
    equal(least_upper_bound(inverse(least_upper_bound(A,least_upper_bound(inverse(B),C))),B),B),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[2,1972]),55]),
    [iquote('para(2,1972),demod([55])')] ).

cnf(7954,plain,
    equal(least_upper_bound(inverse(least_upper_bound(A,least_upper_bound(B,C))),inverse(B)),inverse(B)),
    inference(para,[status(thm),theory(equality)],[57,7935]),
    [iquote('para(57,7935)')] ).

cnf(7966,plain,
    equal(least_upper_bound(inverse(least_upper_bound(A,B)),inverse(B)),inverse(B)),
    inference(para,[status(thm),theory(equality)],[8,7954]),
    [iquote('para(8,7954)')] ).

cnf(12544,plain,
    equal(least_upper_bound(identity,multiply(inverse(A),multiply(b,A))),multiply(inverse(A),multiply(b,A))),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1673,7966]),51,439,439,57,57,3,439,439,57,57,3]),
    [iquote('para(1673,7966),demod([51,439,439,57,57,3,439,439,57,57,3])')] ).

cnf(12545,plain,
    $false,
    inference(conflict,[status(thm)],[12544,17]),
    [iquote('conflict(12544,17)')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP175-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13  % Command  : tptp2X_and_run_eqp %s
% 0.13/0.34  % Computer : n019.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 13 05:06:24 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 4.16/4.61  ----- EQP 0.9e, May 2009 -----
% 4.16/4.61  The job began on n019.cluster.edu, Mon Jun 13 05:06:25 2022
% 4.16/4.61  The command was "./eqp09e".
% 4.16/4.61  
% 4.16/4.61  set(prolog_style_variables).
% 4.16/4.61  set(lrpo).
% 4.16/4.61  set(basic_paramod).
% 4.16/4.61  set(functional_subsume).
% 4.16/4.61  set(ordered_paramod).
% 4.16/4.61  set(prime_paramod).
% 4.16/4.61  set(para_pairs).
% 4.16/4.61  assign(pick_given_ratio,4).
% 4.16/4.61  clear(print_kept).
% 4.16/4.61  clear(print_new_demod).
% 4.16/4.61  clear(print_back_demod).
% 4.16/4.61  clear(print_given).
% 4.16/4.61  assign(max_mem,64000).
% 4.16/4.61  end_of_commands.
% 4.16/4.61  
% 4.16/4.61  Usable:
% 4.16/4.61  end_of_list.
% 4.16/4.61  
% 4.16/4.61  Sos:
% 4.16/4.61  0 (wt=-1) [] multiply(identity,A) = A.
% 4.16/4.61  0 (wt=-1) [] multiply(inverse(A),A) = identity.
% 4.16/4.61  0 (wt=-1) [] multiply(multiply(A,B),C) = multiply(A,multiply(B,C)).
% 4.16/4.61  0 (wt=-1) [] greatest_lower_bound(A,B) = greatest_lower_bound(B,A).
% 4.16/4.61  0 (wt=-1) [] least_upper_bound(A,B) = least_upper_bound(B,A).
% 4.16/4.61  0 (wt=-1) [] greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(greatest_lower_bound(A,B),C).
% 4.16/4.61  0 (wt=-1) [] least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C).
% 4.16/4.61  0 (wt=-1) [] least_upper_bound(A,A) = A.
% 4.16/4.61  0 (wt=-1) [] greatest_lower_bound(A,A) = A.
% 4.16/4.61  0 (wt=-1) [] least_upper_bound(A,greatest_lower_bound(A,B)) = A.
% 4.16/4.61  0 (wt=-1) [] greatest_lower_bound(A,least_upper_bound(A,B)) = A.
% 4.16/4.61  0 (wt=-1) [] multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)).
% 4.16/4.61  0 (wt=-1) [] multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 4.16/4.61  0 (wt=-1) [] multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)).
% 4.16/4.61  0 (wt=-1) [] multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 4.16/4.61  0 (wt=-1) [] greatest_lower_bound(identity,b) = identity.
% 4.16/4.61  0 (wt=-1) [] -(least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = multiply(inverse(a),multiply(b,a))).
% 4.16/4.61  end_of_list.
% 4.16/4.61  
% 4.16/4.61  Demodulators:
% 4.16/4.61  end_of_list.
% 4.16/4.61  
% 4.16/4.61  Passive:
% 4.16/4.61  end_of_list.
% 4.16/4.61  
% 4.16/4.61  Starting to process input.
% 4.16/4.61  
% 4.16/4.61  ** KEPT: 1 (wt=5) [] multiply(identity,A) = A.
% 4.16/4.61  1 is a new demodulator.
% 4.16/4.61  
% 4.16/4.61  ** KEPT: 2 (wt=6) [] multiply(inverse(A),A) = identity.
% 4.16/4.61  2 is a new demodulator.
% 4.16/4.61  
% 4.16/4.61  ** KEPT: 3 (wt=11) [] multiply(multiply(A,B),C) = multiply(A,multiply(B,C)).
% 4.16/4.61  3 is a new demodulator.
% 4.16/4.61  
% 4.16/4.61  ** KEPT: 4 (wt=7) [] greatest_lower_bound(A,B) = greatest_lower_bound(B,A).
% 4.16/4.61  clause forward subsumed: 0 (wt=7) [flip(4)] greatest_lower_bound(B,A) = greatest_lower_bound(A,B).
% 4.16/4.61  
% 4.16/4.61  ** KEPT: 5 (wt=7) [] least_upper_bound(A,B) = least_upper_bound(B,A).
% 4.16/4.61  clause forward subsumed: 0 (wt=7) [flip(5)] least_upper_bound(B,A) = least_upper_bound(A,B).
% 4.16/4.61  
% 4.16/4.61  ** KEPT: 6 (wt=11) [flip(1)] greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)).
% 4.16/4.61  6 is a new demodulator.
% 4.16/4.61  
% 4.16/4.61  ** KEPT: 7 (wt=11) [flip(1)] least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)).
% 4.16/4.61  7 is a new demodulator.
% 4.16/4.61  
% 4.16/4.61  ** KEPT: 8 (wt=5) [] least_upper_bound(A,A) = A.
% 4.16/4.61  8 is a new demodulator.
% 4.16/4.61  
% 4.16/4.61  ** KEPT: 9 (wt=5) [] greatest_lower_bound(A,A) = A.
% 4.16/4.61  9 is a new demodulator.
% 4.16/4.61  
% 4.16/4.61  ** KEPT: 10 (wt=7) [] least_upper_bound(A,greatest_lower_bound(A,B)) = A.
% 4.16/4.61  10 is a new demodulator.
% 4.16/4.61  
% 4.16/4.61  ** KEPT: 11 (wt=7) [] greatest_lower_bound(A,least_upper_bound(A,B)) = A.
% 4.16/4.61  11 is a new demodulator.
% 4.16/4.61  
% 4.16/4.61  ** KEPT: 12 (wt=13) [] multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)).
% 4.16/4.61  12 is a new demodulator.
% 4.16/4.61  
% 4.16/4.61  ** KEPT: 13 (wt=13) [] multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 4.16/4.61  13 is a new demodulator.
% 4.16/4.61  
% 4.16/4.61  ** KEPT: 14 (wt=13) [] multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)).
% 4.16/4.61  14 is a new demodulator.
% 4.16/4.61  
% 4.16/4.61  ** KEPT: 15 (wt=13) [] multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 4.16/4.61  15 is a new demodulator.
% 4.16/4.61  
% 4.16/4.61  ** KEPT: 16 (wt=5) [] greatest_lower_bound(identity,b) = identity.
% 4.16/4.61  16 is a new demodulator.
% 4.16/4.61  
% 4.16/4.61  ** KEPT: 17 (wt=15) [] -(least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = multiply(inverse(a),multiply(b,a))).
% 4.16/4.61  ---------------- PROOF FOUND ----------------
% 4.16/4.61  % SZS status Unsatisfiable
% 4.16/4.61  
% 4.16/4.61  
% 4.16/4.61  After processing input:
% 4.16/4.61  
% 4.16/4.61  Usable:
% 4.16/4.61  end_of_list.
% 4.16/4.61  
% 4.16/4.61  Sos:
% 4.16/4.61  1 (wt=5) [] multiply(identity,A) = A.
% 4.16/4.61  8 (wt=5) [] least_upper_bound(A,A) = A.
% 4.16/4.61  9 (wt=5) [] greatest_lower_bound(A,A) = A.
% 4.16/4.61  16 (wt=5) [] greatest_lower_bound(identity,b) = identity.
% 4.16/4.61  2 (wt=6) [] multiply(inverse(A),A) = identity.
% 4.16/4.61  4 (wt=7) [] greatest_lower_bound(A,B) = greatest_lower_bound(B,A).
% 4.16/4.61  5 (wt=7) [] least_upper_bound(A,B) = least_upper_bound(B,A).
% 4.16/4.61  10 (wt=7) [] least_upper_bound(A,greatest_lower_bound(A,B)) = A.
% 4.16/4.61  11 (wt=7) [] greatest_lower_bound(A,least_upper_bound(A,B)) = A.
% 4.16/4.61  3 (wt=11) [] multiply(multiply(A,B),C) = multiply(A,multiply(B,C)).
% 4.16/4.61  6 (wt=11) [flip(1)] greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)).
% 4.16/4.61  7 (wt=11) [flip(1)] least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)).
% 4.16/4.61  12 (wt=13) [] multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)).
% 4.16/4.61  13 (wt=13) [] multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 4.16/4.61  14 (wt=13) [] multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)).
% 4.16/4.61  15 (wt=13) [] multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 4.16/4.61  17 (wt=15) [] -(least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = multiply(inverse(a),multiply(b,a))).
% 4.16/4.61  end_of_list.
% 4.16/4.61  
% 4.16/4.61  Demodulators:
% 4.16/4.61  1 (wt=5) [] multiply(identity,A) = A.
% 4.16/4.61  2 (wt=6) [] multiply(inverse(A),A) = identity.
% 4.16/4.61  3 (wt=11) [] multiply(multiply(A,B),C) = multiply(A,multiply(B,C)).
% 4.16/4.61  6 (wt=11) [flip(1)] greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)).
% 4.16/4.61  7 (wt=11) [flip(1)] least_upper_bound(least_upper_bound(A,B),C) = least_upper_bound(A,least_upper_bound(B,C)).
% 4.16/4.61  8 (wt=5) [] least_upper_bound(A,A) = A.
% 4.16/4.61  9 (wt=5) [] greatest_lower_bound(A,A) = A.
% 4.16/4.61  10 (wt=7) [] least_upper_bound(A,greatest_lower_bound(A,B)) = A.
% 4.16/4.61  11 (wt=7) [] greatest_lower_bound(A,least_upper_bound(A,B)) = A.
% 4.16/4.61  12 (wt=13) [] multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)).
% 4.16/4.61  13 (wt=13) [] multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)).
% 4.16/4.61  14 (wt=13) [] multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)).
% 4.16/4.61  15 (wt=13) [] multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)).
% 4.16/4.61  16 (wt=5) [] greatest_lower_bound(identity,b) = identity.
% 4.16/4.61  end_of_list.
% 4.16/4.61  
% 4.16/4.61  Passive:
% 4.16/4.61  end_of_list.
% 4.16/4.61  
% 4.16/4.61  UNIT CONFLICT from 12544 and 17 at   2.31 seconds.
% 4.16/4.61  
% 4.16/4.61  ---------------- PROOF ----------------
% 4.16/4.61  % SZS output start Refutation
% See solution above
% 4.16/4.61  ------------ end of proof -------------
% 4.16/4.61  
% 4.16/4.61  
% 4.16/4.61  ------------- memory usage ------------
% 4.16/4.61  Memory dynamically allocated (tp_alloc): 25878.
% 4.16/4.61    type (bytes each)        gets      frees     in use      avail      bytes
% 4.16/4.61  sym_ent (  96)               58          0         58          0      5.4 K
% 4.16/4.61  term (  16)             1886625    1530348     356277         39   6910.3 K
% 4.16/4.61  gen_ptr (   8)          1919914     263398    1656516         42  12941.9 K
% 4.16/4.61  context ( 808)          2424915    2424913          2          6      6.3 K
% 4.16/4.61  trail (  12)             130341     130341          0          7      0.1 K
% 4.16/4.61  bt_node (  68)          1266444    1266441          3         24      1.8 K
% 4.16/4.61  ac_position (285432)          0          0          0          0      0.0 K
% 4.16/4.61  ac_match_pos (14044)          0          0          0          0      0.0 K
% 4.16/4.61  ac_match_free_vars_pos (4020)
% 4.16/4.61                                0          0          0          0      0.0 K
% 4.16/4.61  discrim (  12)           288941      10545     278396        157   3264.3 K
% 4.16/4.61  flat (  40)             4205996    4205996          0        185      7.2 K
% 4.16/4.61  discrim_pos (  12)        91613      91613          0          1      0.0 K
% 4.16/4.61  fpa_head (  12)           24140          0      24140          0    282.9 K
% 4.16/4.61  fpa_tree (  28)           54279      54279          0         83      2.3 K
% 4.16/4.61  fpa_pos (  36)            21166      21166          0          1      0.0 K
% 4.16/4.61  literal (  12)            73577      61033      12544          1    147.0 K
% 4.16/4.61  clause (  24)             73577      61033      12544          1    294.0 K
% 4.16/4.61  list (  12)                8681       8625         56          3      0.7 K
% 4.16/4.61  list_pos (  20)           47960       3612      44348          0    866.2 K
% 4.16/4.61  pair_index (   40)              2          0          2          0      0.1 K
% 4.16/4.61  
% 4.16/4.61  -------------- statistics -------------
% 4.16/4.61  Clauses input                 17
% 4.16/4.61    Usable input                   0
% 4.16/4.61    Sos input                     17
% 4.16/4.61    Demodulators input             0
% 4.16/4.61    Passive input                  0
% 4.16/4.61  
% 4.16/4.61  Processed BS (before search)  19
% 4.16/4.61  Forward subsumed BS            2
% 4.16/4.61  Kept BS                       17
% 4.16/4.61  New demodulators BS           14
% 4.16/4.61  Back demodulated BS            0
% 4.16/4.61  
% 4.16/4.61  Clauses or pairs given    245452
% 4.16/4.61  Clauses generated          50289
% 4.16/4.61  Forward subsumed           37762
% 4.16/4.61  Deleted by weight              0
% 4.16/4.61  Deleted by variable count      0
% 4.16/4.61  Kept                       12527
% 4.16/4.61  New demodulators            8608
% 4.16/4.61  Back demodulated             843
% 4.16/4.61  Ordered paramod prunes         0
% 4.16/4.61  Basic paramod prunes     1493642
% 4.16/4.61  Prime paramod prunes        5297
% 4.16/4.61  Semantic prunes                0
% 4.16/4.61  
% 4.16/4.61  Rewrite attmepts          722195
% 4.16/4.61  Rewrites                   77842
% 4.16/4.61  
% 4.16/4.61  FPA overloads                  0
% 4.16/4.61  FPA underloads                 0
% 4.16/4.61  
% 4.16/4.61  Usable size                    0
% 4.16/4.61  Sos size                   11700
% 4.16/4.61  Demodulators size           8405
% 4.16/4.61  Passive size                   0
% 4.16/4.61  Disabled size                843
% 4.16/4.61  
% 4.16/4.61  Proofs found                   1
% 4.16/4.61  
% 4.16/4.61  ----------- times (seconds) ----------- Mon Jun 13 05:06:29 2022
% 4.16/4.61  
% 4.16/4.61  user CPU time             2.31   (0 hr, 0 min, 2 sec)
% 4.16/4.61  system CPU time           1.20   (0 hr, 0 min, 1 sec)
% 4.16/4.61  wall-clock time           4      (0 hr, 0 min, 4 sec)
% 4.16/4.61  input time                0.00
% 4.16/4.61  paramodulation time       0.35
% 4.16/4.61  demodulation time         0.18
% 4.16/4.61  orient time               0.08
% 4.16/4.61  weigh time                0.03
% 4.16/4.61  forward subsume time      0.04
% 4.16/4.61  back demod find time      0.13
% 4.16/4.61  conflict time             0.01
% 4.16/4.61  LRPO time                 0.03
% 4.16/4.61  store clause time         1.04
% 4.16/4.61  disable clause time       0.06
% 4.16/4.61  prime paramod time        0.06
% 4.16/4.61  semantics time            0.00
% 4.16/4.61  
% 4.16/4.61  EQP interrupted
%------------------------------------------------------------------------------