%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SCT007-1 : TPTP v8.1.0. Released v4.1.0.
% 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 : Mon Jul 18 22:12:59 EDT 2022

% Result   : Unsatisfiable 0.40s 0.58s
% Output   : Refutation 0.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (   9 unt;   0 nHn;  10 RR)
%            Number of literals    :   11 (   0 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   7 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(29,axiom,
    equal(c_Collect(u,v),u),
    file('SCT007-1.p',unknown),
    [] ).

cnf(562,axiom,
    equal(c_Collect(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_OLin),
    file('SCT007-1.p',unknown),
    [] ).

cnf(569,axiom,
    ( ~ hBOOL(c_Order__Relation_Olinear__order__on(u,v,w))
    | hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(u,w),c_HOL_Ominus__class_Ominus(v,c_Relation_OId(w),tc_fun(tc_prod(w,w),tc_bool)))) ),
    file('SCT007-1.p',unknown),
    [] ).

cnf(603,axiom,
    hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt)),
    file('SCT007-1.p',unknown),
    [] ).

cnf(605,axiom,
    ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),u)),
    file('SCT007-1.p',unknown),
    [] ).

cnf(609,plain,
    equal(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin),
    inference(rew,[status(thm),theory(equality)],[29,562]),
    [iquote('0:Rew:29.0,562.0')] ).

cnf(610,plain,
    ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,u)),
    inference(rew,[status(thm),theory(equality)],[609,605]),
    [iquote('0:Rew:609.0,605.0')] ).

cnf(657,plain,
    hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
    inference(res,[status(thm),theory(equality)],[603,569]),
    [iquote('0:Res:603.0,569.0')] ).

cnf(680,plain,
    hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
    inference(rew,[status(thm),theory(equality)],[609,657]),
    [iquote('0:Rew:609.0,657.0')] ).

cnf(681,plain,
    $false,
    inference(mrr,[status(thm)],[680,610]),
    [iquote('0:MRR:680.0,610.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SCT007-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.11/0.33  % Computer : n025.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Sat Jul  2 03:18:54 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.40/0.58  
% 0.40/0.58  SPASS V 3.9 
% 0.40/0.58  SPASS beiseite: Proof found.
% 0.40/0.58  % SZS status Theorem
% 0.40/0.58  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.40/0.58  SPASS derived 28 clauses, backtracked 0 clauses, performed 0 splits and kept 540 clauses.
% 0.40/0.58  SPASS allocated 76815 KBytes.
% 0.40/0.58  SPASS spent	0:00:00.22 on the problem.
% 0.40/0.58  		0:00:00.06 for the input.
% 0.40/0.58  		0:00:00.00 for the FLOTTER CNF translation.
% 0.40/0.58  		0:00:00.00 for inferences.
% 0.40/0.58  		0:00:00.00 for the backtracking.
% 0.40/0.58  		0:00:00.10 for the reduction.
% 0.40/0.58  
% 0.40/0.58  
% 0.40/0.58  Here is a proof with depth 1, length 10 :
% 0.40/0.58  % SZS output start Refutation
% See solution above
% 0.40/0.58  Formulae used in the proof : cls_Collect__def_0 cls_Lin__def_0 cls_strict__linear__order__on__diff__Id_0 cls_conjecture_0 cls_conjecture_2
% 0.40/0.58  
%------------------------------------------------------------------------------