TSTP Solution File: SYN084-2 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SYN084-2 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 21 12:18:30 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   27 (  15 unt;   4 nHn;  27 RR)
%            Number of literals    :   46 (   0 equ;  22 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    big_p(a),
    file('SYN084-2.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ big_p(a)
    | big_p(f(f(u)))
    | big_p(u) ),
    file('SYN084-2.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ big_p(f(u))
    | ~ big_p(a)
    | big_p(f(f(u))) ),
    file('SYN084-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ big_p(f(f(sk2)))
    | ~ big_p(f(f(sk1))) ),
    file('SYN084-2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ big_p(sk2)
    | ~ big_p(sk1)
    | big_p(f(sk2))
    | big_p(f(sk1)) ),
    file('SYN084-2.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ big_p(sk1)
    | ~ big_p(f(f(sk2)))
    | big_p(f(sk1)) ),
    file('SYN084-2.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ big_p(sk2)
    | ~ big_p(f(f(sk1)))
    | big_p(f(sk2)) ),
    file('SYN084-2.p',unknown),
    [] ).

cnf(8,plain,
    ( big_p(u)
    | big_p(f(f(u))) ),
    inference(mrr,[status(thm)],[2,1]),
    [iquote('0:MRR:2.0,1.0')] ).

cnf(9,plain,
    ( ~ big_p(f(u))
    | big_p(f(f(u))) ),
    inference(mrr,[status(thm)],[3,1]),
    [iquote('0:MRR:3.1,1.0')] ).

cnf(10,plain,
    ~ big_p(f(f(sk2))),
    inference(spt,[spt(split,[position(s1)])],[4]),
    [iquote('1:Spt:4.0')] ).

cnf(11,plain,
    ~ big_p(f(sk2)),
    inference(res,[status(thm),theory(equality)],[9,10]),
    [iquote('1:Res:9.1,10.0')] ).

cnf(12,plain,
    big_p(sk2),
    inference(res,[status(thm),theory(equality)],[8,10]),
    [iquote('1:Res:8.1,10.0')] ).

cnf(13,plain,
    ( ~ big_p(f(f(sk1)))
    | big_p(f(sk2)) ),
    inference(mrr,[status(thm)],[7,12]),
    [iquote('1:MRR:7.0,12.0')] ).

cnf(14,plain,
    ( ~ big_p(sk1)
    | big_p(f(sk2))
    | big_p(f(sk1)) ),
    inference(mrr,[status(thm)],[5,12]),
    [iquote('1:MRR:5.0,12.0')] ).

cnf(15,plain,
    ~ big_p(f(f(sk1))),
    inference(mrr,[status(thm)],[13,11]),
    [iquote('1:MRR:13.1,11.0')] ).

cnf(16,plain,
    ( ~ big_p(sk1)
    | big_p(f(sk1)) ),
    inference(mrr,[status(thm)],[14,11]),
    [iquote('1:MRR:14.1,11.0')] ).

cnf(17,plain,
    ~ big_p(f(sk1)),
    inference(res,[status(thm),theory(equality)],[9,15]),
    [iquote('1:Res:9.1,15.0')] ).

cnf(18,plain,
    big_p(sk1),
    inference(res,[status(thm),theory(equality)],[8,15]),
    [iquote('1:Res:8.1,15.0')] ).

cnf(19,plain,
    big_p(f(sk1)),
    inference(mrr,[status(thm)],[16,18]),
    [iquote('1:MRR:16.0,18.0')] ).

cnf(20,plain,
    $false,
    inference(mrr,[status(thm)],[17,19]),
    [iquote('1:MRR:17.0,19.0')] ).

cnf(21,plain,
    big_p(f(f(sk2))),
    inference(spt,[spt(split,[position(sa)])],[20,10]),
    [iquote('1:Spt:20.0,4.0,10.0')] ).

cnf(22,plain,
    ~ big_p(f(f(sk1))),
    inference(spt,[spt(split,[position(s2)])],[4]),
    [iquote('1:Spt:20.0,4.1')] ).

cnf(23,plain,
    ( ~ big_p(sk1)
    | big_p(f(sk1)) ),
    inference(mrr,[status(thm)],[6,21]),
    [iquote('1:MRR:6.1,21.0')] ).

cnf(24,plain,
    ~ big_p(f(sk1)),
    inference(res,[status(thm),theory(equality)],[9,22]),
    [iquote('1:Res:9.1,22.0')] ).

cnf(25,plain,
    big_p(sk1),
    inference(res,[status(thm),theory(equality)],[8,22]),
    [iquote('1:Res:8.1,22.0')] ).

cnf(26,plain,
    big_p(f(sk1)),
    inference(mrr,[status(thm)],[23,25]),
    [iquote('1:MRR:23.0,25.0')] ).

cnf(27,plain,
    $false,
    inference(mrr,[status(thm)],[24,26]),
    [iquote('1:MRR:24.0,26.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SYN084-2 : TPTP v8.1.0. Released v1.2.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n020.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 : Tue Jul 12 01:16:57 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.42  
% 0.19/0.42  SPASS V 3.9 
% 0.19/0.42  SPASS beiseite: Proof found.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.42  SPASS derived 11 clauses, backtracked 5 clauses, performed 1 splits and kept 21 clauses.
% 0.19/0.42  SPASS allocated 63091 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.42  		0:00:00.04 for the input.
% 0.19/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42  		0:00:00.00 for inferences.
% 0.19/0.42  		0:00:00.00 for the backtracking.
% 0.19/0.42  		0:00:00.00 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 2, length 27 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : pel62_1 pel62_2 pel62_3 pel62_4 pel62_5 pel62_6 pel62_7
% 0.19/0.42  
%------------------------------------------------------------------------------