TSTP Solution File: SCT058-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SCT058-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.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 : Mon Jul 18 22:13:15 EDT 2022

% Result   : Unsatisfiable 40.75s 41.02s
% Output   : Refutation 40.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   19 (  11 unt;   2 nHn;  19 RR)
%            Number of literals    :   27 (   0 equ;  12 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   22 (  22 usr;  15 con; 0-5 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(597,axiom,
    ( ~ hBOOL(c_in(c_Pair(u,v,w,x),y,tc_prod(w,x)))
    | hBOOL(c_in(c_Pair(v,u,x,w),hAPP(c_Relation_Oconverse(w,x),y),tc_prod(x,w))) ),
    file('SCT058-1.p',unknown),
    [] ).

cnf(599,axiom,
    ( ~ hBOOL(c_in(c_Pair(u,v,w,x),hAPP(c_Relation_Oconverse(x,w),y),tc_prod(w,x)))
    | hBOOL(c_in(c_Pair(v,u,x,w),y,tc_prod(x,w))) ),
    file('SCT058-1.p',unknown),
    [] ).

cnf(602,axiom,
    ( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,u),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,u),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('SCT058-1.p',unknown),
    [] ).

cnf(603,axiom,
    ( ~ hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,u),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,u),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('SCT058-1.p',unknown),
    [] ).

cnf(607,axiom,
    equal(hAPP(c_Fun_Ocomp(u,v,w,x,y),z),hAPP(u,hAPP(v,z))),
    file('SCT058-1.p',unknown),
    [] ).

cnf(640,axiom,
    ( hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('SCT058-1.p',unknown),
    [] ).

cnf(641,axiom,
    ( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('SCT058-1.p',unknown),
    [] ).

cnf(683,plain,
    ( hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(rew,[status(thm),theory(equality)],[607,640]),
    [iquote('0:Rew:607.0,640.1')] ).

cnf(684,plain,
    ( ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(rew,[status(thm),theory(equality)],[607,641]),
    [iquote('0:Rew:607.0,641.1')] ).

cnf(64372,plain,
    hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(spt,[spt(split,[position(s1)])],[683]),
    [iquote('1:Spt:683.0')] ).

cnf(64373,plain,
    ~ hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(mrr,[status(thm)],[684,64372]),
    [iquote('1:MRR:684.0,64372.0')] ).

cnf(64399,plain,
    hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(res,[status(thm),theory(equality)],[64372,602]),
    [iquote('1:Res:64372.0,602.0')] ).

cnf(64415,plain,
    ~ hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(res,[status(thm),theory(equality)],[597,64373]),
    [iquote('1:Res:597.1,64373.0')] ).

cnf(64416,plain,
    $false,
    inference(mrr,[status(thm)],[64415,64399]),
    [iquote('1:MRR:64415.0,64399.0')] ).

cnf(64417,plain,
    ~ hBOOL(c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(spt,[spt(split,[position(sa)])],[64416,64372]),
    [iquote('1:Spt:64416.0,683.0,64372.0')] ).

cnf(64418,plain,
    hBOOL(c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(spt,[spt(split,[position(s2)])],[683]),
    [iquote('1:Spt:64416.0,683.1')] ).

cnf(64443,plain,
    hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(res,[status(thm),theory(equality)],[64418,599]),
    [iquote('1:Res:64418.0,599.0')] ).

cnf(64476,plain,
    ~ hBOOL(c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,v_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(res,[status(thm),theory(equality)],[603,64417]),
    [iquote('1:Res:603.1,64417.0')] ).

cnf(64477,plain,
    $false,
    inference(mrr,[status(thm)],[64476,64443]),
    [iquote('1:MRR:64476.0,64443.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SCT058-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n024.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Fri Jul  1 23:01:30 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 40.75/41.02  
% 40.75/41.02  SPASS V 3.9 
% 40.75/41.02  SPASS beiseite: Proof found.
% 40.75/41.02  % SZS status Theorem
% 40.75/41.02  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 40.75/41.02  SPASS derived 49959 clauses, backtracked 3 clauses, performed 1 splits and kept 11498 clauses.
% 40.75/41.02  SPASS allocated 133021 KBytes.
% 40.75/41.02  SPASS spent	0:0:38.87 on the problem.
% 40.75/41.02  		0:00:00.06 for the input.
% 40.75/41.02  		0:00:00.00 for the FLOTTER CNF translation.
% 40.75/41.02  		0:00:00.70 for inferences.
% 40.75/41.02  		0:00:00.03 for the backtracking.
% 40.75/41.02  		0:0:37.69 for the reduction.
% 40.75/41.02  
% 40.75/41.02  
% 40.75/41.02  Here is a proof with depth 2, length 19 :
% 40.75/41.02  % SZS output start Refutation
% See solution above
% 40.75/41.02  Formulae used in the proof : cls_converse__iff_1 cls_converseD_0 cls_iff_1 cls_iff_0 cls_o__apply_0 cls_conjecture_0 cls_conjecture_1
% 40.75/41.02  
%------------------------------------------------------------------------------