TSTP Solution File: ALG029+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG029+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 18:02:01 EDT 2022

% Result   : Theorem 0.19s 0.44s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   18 (   4 unt;   0 nHn;  18 RR)
%            Number of literals    :   49 (   0 equ;  34 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    sorti2(skc3),
    file('ALG029+1.p',unknown),
    [] ).

cnf(2,axiom,
    sorti2(skc2),
    file('ALG029+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ sorti2(u)
    | sorti1(j(u)) ),
    file('ALG029+1.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ sorti2(u)
    | equal(h(j(u)),u) ),
    file('ALG029+1.p',unknown),
    [] ).

cnf(7,axiom,
    ~ equal(op2(skc3,skc2),op2(skc2,skc3)),
    file('ALG029+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ sorti2(u)
    | ~ sorti2(v)
    | sorti2(op2(v,u)) ),
    file('ALG029+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ sorti1(u)
    | ~ sorti1(v)
    | equal(op1(v,u),op1(u,v)) ),
    file('ALG029+1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ sorti2(u)
    | ~ sorti2(v)
    | equal(op1(j(v),j(u)),j(op2(v,u))) ),
    file('ALG029+1.p',unknown),
    [] ).

cnf(35,plain,
    ( ~ sorti2(u)
    | ~ sorti2(v)
    | ~ sorti1(j(v))
    | ~ sorti1(j(u))
    | equal(op1(j(u),j(v)),j(op2(v,u))) ),
    inference(spr,[status(thm),theory(equality)],[12,10]),
    [iquote('0:SpR:12.2,10.2')] ).

cnf(42,plain,
    ( ~ sorti2(u)
    | ~ sorti2(v)
    | ~ sorti1(j(v))
    | ~ sorti1(j(u))
    | equal(j(op2(u,v)),j(op2(v,u))) ),
    inference(rew,[status(thm),theory(equality)],[12,35]),
    [iquote('0:Rew:12.2,35.4')] ).

cnf(43,plain,
    ( ~ sorti2(u)
    | ~ sorti2(v)
    | equal(j(op2(u,v)),j(op2(v,u))) ),
    inference(ssi,[status(thm)],[42,4]),
    [iquote('0:SSi:42.3,42.2,4.1,4.1')] ).

cnf(53,plain,
    ( ~ sorti2(u)
    | ~ sorti2(v)
    | ~ sorti2(op2(v,u))
    | equal(h(j(op2(u,v))),op2(v,u)) ),
    inference(spr,[status(thm),theory(equality)],[43,5]),
    [iquote('0:SpR:43.2,5.1')] ).

cnf(61,plain,
    ( ~ sorti2(u)
    | ~ sorti2(v)
    | equal(h(j(op2(u,v))),op2(v,u)) ),
    inference(ssi,[status(thm)],[53,9]),
    [iquote('0:SSi:53.2,9.2')] ).

cnf(66,plain,
    ( ~ sorti2(u)
    | ~ sorti2(v)
    | ~ sorti2(op2(u,v))
    | equal(op2(v,u),op2(u,v)) ),
    inference(spr,[status(thm),theory(equality)],[61,5]),
    [iquote('0:SpR:61.2,5.1')] ).

cnf(70,plain,
    ( ~ sorti2(u)
    | ~ sorti2(v)
    | equal(op2(v,u),op2(u,v)) ),
    inference(ssi,[status(thm)],[66,9]),
    [iquote('0:SSi:66.2,9.2')] ).

cnf(125,plain,
    ( ~ sorti2(skc2)
    | ~ sorti2(skc3)
    | ~ equal(op2(skc2,skc3),op2(skc2,skc3)) ),
    inference(spl,[status(thm),theory(equality)],[70,7]),
    [iquote('0:SpL:70.2,7.0')] ).

cnf(127,plain,
    ( ~ sorti2(skc2)
    | ~ sorti2(skc3) ),
    inference(obv,[status(thm),theory(equality)],[125]),
    [iquote('0:Obv:125.2')] ).

cnf(128,plain,
    $false,
    inference(ssi,[status(thm)],[127,1,2]),
    [iquote('0:SSi:127.1,127.0,1.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : ALG029+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n025.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Thu Jun  9 03:36:20 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.44  
% 0.19/0.44  SPASS V 3.9 
% 0.19/0.44  SPASS beiseite: Proof found.
% 0.19/0.44  % SZS status Theorem
% 0.19/0.44  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.44  SPASS derived 73 clauses, backtracked 0 clauses, performed 0 splits and kept 31 clauses.
% 0.19/0.44  SPASS allocated 103991 KBytes.
% 0.19/0.44  SPASS spent	0:00:00.09 on the problem.
% 0.19/0.44  		0:00:00.03 for the input.
% 0.19/0.44  		0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.44  		0:00:00.00 for inferences.
% 0.19/0.44  		0:00:00.00 for the backtracking.
% 0.19/0.44  		0:00:00.01 for the reduction.
% 0.19/0.44  
% 0.19/0.44  
% 0.19/0.44  Here is a proof with depth 4, length 18 :
% 0.19/0.44  % SZS output start Refutation
% See solution above
% 0.19/0.44  Formulae used in the proof : ax4 co1 ax2 ax3
% 0.19/0.44  
%------------------------------------------------------------------------------