TSTP Solution File: ALG070+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG070+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %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 : Thu Jul 14 18:02:13 EDT 2022

% Result   : Theorem 0.20s 0.47s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   26 (   4 unt;   0 nHn;  26 RR)
%            Number of literals    :   72 (   0 equ;  49 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    sorti2(skc1),
    file('ALG070+1.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ sorti1(u)
    | sorti2(h(u)) ),
    file('ALG070+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ sorti2(u)
    | sorti1(j(u)) ),
    file('ALG070+1.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ sorti2(u)
    | equal(h(j(u)),u) ),
    file('ALG070+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ sorti1(u)
    | equal(j(h(u)),u) ),
    file('ALG070+1.p',unknown),
    [] ).

cnf(7,axiom,
    ~ equal(op2(skc1,op2(skc1,skc1)),skc1),
    file('ALG070+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ sorti2(u)
    | ~ sorti2(v)
    | sorti2(op2(v,u)) ),
    file('ALG070+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ sorti1(u)
    | ~ sorti1(op1(u,u))
    | equal(op1(u,op1(u,u)),u) ),
    file('ALG070+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ sorti1(u)
    | ~ sorti1(v)
    | equal(op2(h(v),h(u)),h(op1(v,u))) ),
    file('ALG070+1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ sorti2(u)
    | ~ sorti2(v)
    | equal(op1(j(v),j(u)),j(op2(v,u))) ),
    file('ALG070+1.p',unknown),
    [] ).

cnf(30,plain,
    ( ~ sorti1(u)
    | ~ sorti2(h(u))
    | ~ sorti2(v)
    | equal(j(op2(v,h(u))),op1(j(v),u)) ),
    inference(spr,[status(thm),theory(equality)],[6,12]),
    [iquote('0:SpR:6.1,12.2')] ).

cnf(34,plain,
    ( ~ sorti1(u)
    | ~ sorti2(v)
    | equal(j(op2(v,h(u))),op1(j(v),u)) ),
    inference(ssi,[status(thm)],[30,3]),
    [iquote('0:SSi:30.1,3.1')] ).

cnf(41,plain,
    ( ~ sorti2(u)
    | ~ sorti1(v)
    | ~ sorti1(j(u))
    | equal(h(op1(j(u),v)),op2(u,h(v))) ),
    inference(spr,[status(thm),theory(equality)],[5,11]),
    [iquote('0:SpR:5.1,11.2')] ).

cnf(43,plain,
    ( ~ sorti2(u)
    | ~ sorti1(v)
    | equal(h(op1(j(u),v)),op2(u,h(v))) ),
    inference(ssi,[status(thm)],[41,4]),
    [iquote('0:SSi:41.2,4.1')] ).

cnf(96,plain,
    ( ~ sorti1(u)
    | ~ sorti2(v)
    | ~ sorti2(op2(v,h(u)))
    | sorti1(op1(j(v),u)) ),
    inference(spr,[status(thm),theory(equality)],[34,4]),
    [iquote('0:SpR:34.2,4.1')] ).

cnf(107,plain,
    ( ~ sorti1(u)
    | ~ sorti2(v)
    | sorti1(op1(j(v),u)) ),
    inference(ssi,[status(thm)],[96,9,3]),
    [iquote('0:SSi:96.2,9.1,3.2')] ).

cnf(145,plain,
    ( ~ sorti1(j(u))
    | ~ sorti2(u)
    | ~ sorti1(op1(j(u),j(u)))
    | ~ sorti1(op1(j(u),j(u)))
    | equal(op2(u,h(op1(j(u),j(u)))),h(j(u))) ),
    inference(spr,[status(thm),theory(equality)],[10,43]),
    [iquote('0:SpR:10.2,43.2')] ).

cnf(159,plain,
    ( ~ sorti1(j(u))
    | ~ sorti2(u)
    | ~ sorti1(op1(j(u),j(u)))
    | equal(op2(u,h(op1(j(u),j(u)))),h(j(u))) ),
    inference(obv,[status(thm),theory(equality)],[145]),
    [iquote('0:Obv:145.2')] ).

cnf(160,plain,
    ( ~ sorti1(j(u))
    | ~ sorti2(u)
    | ~ sorti1(op1(j(u),j(u)))
    | equal(op2(u,op2(u,u)),u) ),
    inference(rew,[status(thm),theory(equality)],[5,159,43]),
    [iquote('0:Rew:5.1,159.3,43.2,159.3,5.1,159.3')] ).

cnf(161,plain,
    ( ~ sorti2(u)
    | ~ sorti1(op1(j(u),j(u)))
    | equal(op2(u,op2(u,u)),u) ),
    inference(ssi,[status(thm)],[160,4]),
    [iquote('0:SSi:160.0,4.1')] ).

cnf(320,plain,
    ( ~ sorti1(j(u))
    | ~ sorti2(u)
    | ~ sorti2(u)
    | equal(op2(u,op2(u,u)),u) ),
    inference(res,[status(thm),theory(equality)],[107,161]),
    [iquote('0:Res:107.2,161.1')] ).

cnf(323,plain,
    ( ~ sorti1(j(u))
    | ~ sorti2(u)
    | equal(op2(u,op2(u,u)),u) ),
    inference(obv,[status(thm),theory(equality)],[320]),
    [iquote('0:Obv:320.1')] ).

cnf(324,plain,
    ( ~ sorti2(u)
    | equal(op2(u,op2(u,u)),u) ),
    inference(ssi,[status(thm)],[323,4]),
    [iquote('0:SSi:323.0,4.1')] ).

cnf(340,plain,
    ( ~ sorti2(skc1)
    | ~ equal(skc1,skc1) ),
    inference(spl,[status(thm),theory(equality)],[324,7]),
    [iquote('0:SpL:324.1,7.0')] ).

cnf(341,plain,
    ~ sorti2(skc1),
    inference(obv,[status(thm),theory(equality)],[340]),
    [iquote('0:Obv:340.1')] ).

cnf(342,plain,
    $false,
    inference(ssi,[status(thm)],[341,1]),
    [iquote('0:SSi:341.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ALG070+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n019.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 : Tue Jun  7 22:03:10 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.47  
% 0.20/0.47  SPASS V 3.9 
% 0.20/0.47  SPASS beiseite: Proof found.
% 0.20/0.47  % SZS status Theorem
% 0.20/0.47  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.47  SPASS derived 193 clauses, backtracked 0 clauses, performed 0 splits and kept 79 clauses.
% 0.20/0.47  SPASS allocated 104331 KBytes.
% 0.20/0.47  SPASS spent	0:00:00.12 on the problem.
% 0.20/0.47  		0:00:00.03 for the input.
% 0.20/0.47  		0:00:00.02 for the FLOTTER CNF translation.
% 0.20/0.47  		0:00:00.00 for inferences.
% 0.20/0.47  		0:00:00.00 for the backtracking.
% 0.20/0.47  		0:00:00.04 for the reduction.
% 0.20/0.47  
% 0.20/0.47  
% 0.20/0.47  Here is a proof with depth 4, length 26 :
% 0.20/0.47  % SZS output start Refutation
% See solution above
% 0.20/0.47  Formulae used in the proof : ax4 co1 ax2 ax3
% 0.20/0.47  
%------------------------------------------------------------------------------