TSTP Solution File: GRP123-7.003 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP123-7.003 : TPTP v8.1.0. Released v1.2.0.
% 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 : Sat Jul 16 11:45:28 EDT 2022

% Result   : Unsatisfiable 0.18s 0.42s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   27 (  11 unt;   8 nHn;  27 RR)
%            Number of literals    :   63 (   0 equ;  24 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   7 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(7,axiom,
    group_element(e_1),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(8,axiom,
    group_element(e_2),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(9,axiom,
    group_element(e_3),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(10,axiom,
    ~ equalish(e_1,e_2),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(11,axiom,
    ~ equalish(e_1,e_3),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(12,axiom,
    ~ equalish(e_2,e_1),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(14,axiom,
    ~ equalish(e_3,e_1),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ group_element(u)
    | ~ group_element(v)
    | product1(v,u,e_3)
    | product1(v,u,e_2)
    | product1(v,u,e_1) ),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ product1(u,v,w)
    | ~ product1(u,x,w)
    | equalish(x,v) ),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ product1(u,v,w)
    | ~ product1(x,v,w)
    | equalish(x,u) ),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(20,axiom,
    product1(u,u,u),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ product2(u,v,w)
    | ~ product2(u,v,x)
    | equalish(x,w) ),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(25,axiom,
    product2(u,u,u),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ product1(u,v,w)
    | ~ product1(x,v,u)
    | product2(w,x,v) ),
    file('GRP123-7.003.p',unknown),
    [] ).

cnf(38,plain,
    ( ~ product2(u,u,v)
    | equalish(v,u) ),
    inference(res,[status(thm),theory(equality)],[25,22]),
    [iquote('0:Res:25.0,22.0')] ).

cnf(40,plain,
    ( ~ product1(u,v,v)
    | equalish(u,v) ),
    inference(res,[status(thm),theory(equality)],[20,19]),
    [iquote('0:Res:20.0,19.0')] ).

cnf(42,plain,
    ( ~ product1(u,v,u)
    | equalish(v,u) ),
    inference(res,[status(thm),theory(equality)],[20,18]),
    [iquote('0:Res:20.0,18.0')] ).

cnf(56,plain,
    ( ~ group_element(e_1)
    | ~ group_element(u)
    | product1(u,e_1,e_3)
    | product1(u,e_1,e_2)
    | equalish(u,e_1) ),
    inference(res,[status(thm),theory(equality)],[16,40]),
    [iquote('0:Res:16.4,40.0')] ).

cnf(65,plain,
    ( ~ group_element(u)
    | product1(u,e_1,e_3)
    | product1(u,e_1,e_2)
    | equalish(u,e_1) ),
    inference(ssi,[status(thm)],[56,7]),
    [iquote('0:SSi:56.0,7.0')] ).

cnf(114,plain,
    ( ~ group_element(e_2)
    | product1(e_2,e_1,e_3)
    | equalish(e_2,e_1)
    | equalish(e_1,e_2) ),
    inference(res,[status(thm),theory(equality)],[65,42]),
    [iquote('0:Res:65.2,42.0')] ).

cnf(115,plain,
    ( product1(e_2,e_1,e_3)
    | equalish(e_2,e_1)
    | equalish(e_1,e_2) ),
    inference(ssi,[status(thm)],[114,8]),
    [iquote('0:SSi:114.0,8.0')] ).

cnf(116,plain,
    product1(e_2,e_1,e_3),
    inference(mrr,[status(thm)],[115,12,10]),
    [iquote('0:MRR:115.1,115.2,12.0,10.0')] ).

cnf(117,plain,
    ( ~ product1(u,e_1,e_2)
    | product2(e_3,u,e_1) ),
    inference(res,[status(thm),theory(equality)],[116,26]),
    [iquote('0:Res:116.0,26.0')] ).

cnf(136,plain,
    ( ~ group_element(u)
    | product1(u,e_1,e_3)
    | equalish(u,e_1)
    | product2(e_3,u,e_1) ),
    inference(res,[status(thm),theory(equality)],[65,117]),
    [iquote('0:Res:65.2,117.0')] ).

cnf(195,plain,
    ( ~ group_element(e_3)
    | product1(e_3,e_1,e_3)
    | equalish(e_3,e_1)
    | equalish(e_1,e_3) ),
    inference(res,[status(thm),theory(equality)],[136,38]),
    [iquote('0:Res:136.3,38.0')] ).

cnf(203,plain,
    ( product1(e_3,e_1,e_3)
    | equalish(e_3,e_1)
    | equalish(e_1,e_3) ),
    inference(ssi,[status(thm)],[195,9]),
    [iquote('0:SSi:195.0,9.0')] ).

cnf(204,plain,
    $false,
    inference(mrr,[status(thm)],[203,42,14,11]),
    [iquote('0:MRR:203.0,203.1,203.2,42.0,14.0,11.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP123-7.003 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.12  % 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 : Mon Jun 13 13:20:24 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.42  
% 0.18/0.42  SPASS V 3.9 
% 0.18/0.42  SPASS beiseite: Proof found.
% 0.18/0.42  % SZS status Theorem
% 0.18/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.42  SPASS derived 136 clauses, backtracked 0 clauses, performed 0 splits and kept 106 clauses.
% 0.18/0.42  SPASS allocated 75758 KBytes.
% 0.18/0.42  SPASS spent	0:00:00.07 on the problem.
% 0.18/0.42  		0:00:00.04 for the input.
% 0.18/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.42  		0:00:00.00 for inferences.
% 0.18/0.42  		0:00:00.00 for the backtracking.
% 0.18/0.42  		0:00:00.02 for the reduction.
% 0.18/0.42  
% 0.18/0.42  
% 0.18/0.42  Here is a proof with depth 6, length 27 :
% 0.18/0.42  % SZS output start Refutation
% See solution above
% 0.18/0.42  Formulae used in the proof : element_1 element_2 element_3 e_1_is_not_e_2 e_1_is_not_e_3 e_2_is_not_e_1 e_3_is_not_e_1 product1_total_function1 product1_right_cancellation product1_left_cancellation product1_idempotence product2_total_function2 product2_idempotence qg1a
% 0.18/0.42  
%------------------------------------------------------------------------------