TSTP Solution File: SCT024-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SCT024-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 22:13:04 EDT 2022

% Result   : Unsatisfiable 0.60s 0.80s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   12 (   9 unt;   2 nHn;  12 RR)
%            Number of literals    :   22 (   0 equ;  11 neg)
%            Maximal clause size   :    6 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   17 (  17 usr;   9 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(672,axiom,
    ( ~ hBOOL(c_in(c_Pair(u,u,v,v),w,tc_prod(v,v)))
    | ~ c_Relation_Oirrefl(w,v) ),
    file('SCT024-1.p',unknown),
    [] ).

cnf(705,axiom,
    c_Relation_Otrans(hAPP(v_P,u),tc_Arrow__Order__Mirabelle_Oalt),
    file('SCT024-1.p',unknown),
    [] ).

cnf(706,axiom,
    c_Relation_Oirrefl(hAPP(v_P,u),tc_Arrow__Order__Mirabelle_Oalt),
    file('SCT024-1.p',unknown),
    [] ).

cnf(707,axiom,
    c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,u),tc_Arrow__Order__Mirabelle_Oalt),
    file('SCT024-1.p',unknown),
    [] ).

cnf(708,axiom,
    hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('SCT024-1.p',unknown),
    [] ).

cnf(709,axiom,
    ~ hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('SCT024-1.p',unknown),
    [] ).

cnf(713,axiom,
    ( ~ hBOOL(c_in(c_Pair(u,v,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(w,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ c_Relation_Otrans(hAPP(w,v_Pa(w)),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Oirrefl(hAPP(w,v_Pa(w)),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(w,v_Pa(w)),tc_Arrow__Order__Mirabelle_Oalt)
    | hBOOL(c_in(c_Pair(u,v,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(w),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | equal(u,v) ),
    file('SCT024-1.p',unknown),
    [] ).

cnf(767,plain,
    ~ hBOOL(c_in(c_Pair(u,u,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(res,[status(thm),theory(equality)],[706,672]),
    [iquote('0:Res:706.0,672.1')] ).

cnf(932,plain,
    ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | equal(v_b,v_a) ),
    inference(res,[status(thm),theory(equality)],[708,713]),
    [iquote('0:Res:708.0,713.0')] ).

cnf(950,plain,
    equal(v_b,v_a),
    inference(mrr,[status(thm)],[932,707,706,705,709]),
    [iquote('0:MRR:932.0,932.1,932.2,932.3,707.0,706.0,705.0,709.0')] ).

cnf(952,plain,
    hBOOL(c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(rew,[status(thm),theory(equality)],[950,708]),
    [iquote('0:Rew:950.0,708.0')] ).

cnf(984,plain,
    $false,
    inference(mrr,[status(thm)],[952,767]),
    [iquote('0:MRR:952.0,767.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SCT024-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n026.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 : Sat Jul  2 08:40:20 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.60/0.80  
% 0.60/0.80  SPASS V 3.9 
% 0.60/0.80  SPASS beiseite: Proof found.
% 0.60/0.80  % SZS status Theorem
% 0.60/0.80  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.60/0.80  SPASS derived 117 clauses, backtracked 0 clauses, performed 0 splits and kept 656 clauses.
% 0.60/0.80  SPASS allocated 77429 KBytes.
% 0.60/0.80  SPASS spent	0:00:00.42 on the problem.
% 0.60/0.80  		0:00:00.07 for the input.
% 0.60/0.80  		0:00:00.00 for the FLOTTER CNF translation.
% 0.60/0.80  		0:00:00.00 for inferences.
% 0.60/0.80  		0:00:00.00 for the backtracking.
% 0.60/0.80  		0:00:00.23 for the reduction.
% 0.60/0.80  
% 0.60/0.80  
% 0.60/0.80  Here is a proof with depth 1, length 12 :
% 0.60/0.80  % SZS output start Refutation
% See solution above
% 0.60/0.80  Formulae used in the proof : cls_irrefl__def_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_8
% 0.60/0.80  
%------------------------------------------------------------------------------