%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LAT271-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n012.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 : Sun Jul 17 06:49:58 EDT 2022

% Result   : Unsatisfiable 0.19s 0.41s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   5 unt;   0 nHn;   7 RR)
%            Number of literals    :   10 (   0 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;  12 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ c_in(u,v,w)
    | ~ c_lessequals(v,c_Tarski_Ointerval(x,y,z,w),tc_set(w))
    | c_in(c_Pair(y,u,w,w),x,tc_prod(w,w)) ),
    file('LAT271-2.p',unknown),
    [] ).

cnf(2,axiom,
    c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
    file('LAT271-2.p',unknown),
    [] ).

cnf(3,axiom,
    c_in(v_x,v_S,t_a),
    file('LAT271-2.p',unknown),
    [] ).

cnf(4,axiom,
    ~ c_in(c_Pair(v_a,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
    file('LAT271-2.p',unknown),
    [] ).

cnf(7,plain,
    ( ~ c_lessequals(u,c_Tarski_Ointerval(v_r,v_a,v,t_a),tc_set(t_a))
    | ~ c_in(v_x,u,t_a) ),
    inference(res,[status(thm),theory(equality)],[1,4]),
    [iquote('0:Res:1.2,4.0')] ).

cnf(8,plain,
    ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,u,t_a),tc_set(t_a)),
    inference(res,[status(thm),theory(equality)],[3,7]),
    [iquote('0:Res:3.0,7.0')] ).

cnf(10,plain,
    $false,
    inference(unc,[status(thm)],[8,2]),
    [iquote('0:UnC:8.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LAT271-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n012.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Wed Jun 29 18:07:33 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.41  
% 0.19/0.41  SPASS V 3.9 
% 0.19/0.41  SPASS beiseite: Proof found.
% 0.19/0.41  % SZS status Theorem
% 0.19/0.41  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.41  SPASS derived 5 clauses, backtracked 0 clauses, performed 0 splits and kept 8 clauses.
% 0.19/0.41  SPASS allocated 63092 KBytes.
% 0.19/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.41  		0:00:00.04 for the input.
% 0.19/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41  		0:00:00.00 for inferences.
% 0.19/0.41  		0:00:00.00 for the backtracking.
% 0.19/0.41  		0:00:00.00 for the reduction.
% 0.19/0.41  
% 0.19/0.41  
% 0.19/0.41  Here is a proof with depth 2, length 7 :
% 0.19/0.41  % SZS output start Refutation
% See solution above
% 0.19/0.41  Formulae used in the proof : cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0 cls_conjecture_2 cls_conjecture_6 cls_conjecture_7
% 0.19/0.41  
%------------------------------------------------------------------------------