%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWV573-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 : Wed Jul 20 21:44:25 EDT 2022

% Result   : Unsatisfiable 0.47s 0.71s
% Output   : Refutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   15 (  14 unt;   0 nHn;  15 RR)
%            Number of literals    :   16 (   0 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(162,axiom,
    equal(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_ORe(c_Complex_Oii)),
    file('SWV573-1.p',unknown),
    [] ).

cnf(600,axiom,
    equal(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(c_Transcendental_Opi)),
    file('SWV573-1.p',unknown),
    [] ).

cnf(881,axiom,
    equal(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi)),
    file('SWV573-1.p',unknown),
    [] ).

cnf(1059,axiom,
    equal(c_Complex_Ocomplex_OComplex(u,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Oof__real(u,tc_Complex_Ocomplex)),
    file('SWV573-1.p',unknown),
    [] ).

cnf(1061,axiom,
    ( ~ class_RealVector_Oreal__algebra__1(u)
    | equal(c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v,tc_RealDef_Oreal),u),c_Nat_Osemiring__1__class_Oof__nat(v,u)) ),
    file('SWV573-1.p',unknown),
    [] ).

cnf(1243,axiom,
    class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
    file('SWV573-1.p',unknown),
    [] ).

cnf(1264,axiom,
    ~ equal(c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex)),
    file('SWV573-1.p',unknown),
    [] ).

cnf(1268,plain,
    equal(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi)),
    inference(rew,[status(thm),theory(equality)],[881,600]),
    [iquote('0:Rew:881.0,600.0')] ).

cnf(1269,plain,
    equal(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(c_Transcendental_Opi)),
    inference(rew,[status(thm),theory(equality)],[1268,881]),
    [iquote('0:Rew:1268.0,881.0')] ).

cnf(1273,plain,
    equal(c_Complex_ORe(c_Complex_Oii),c_Transcendental_Osin(c_Transcendental_Opi)),
    inference(rew,[status(thm),theory(equality)],[162,1269]),
    [iquote('0:Rew:162.0,1269.0')] ).

cnf(1274,plain,
    equal(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(c_Transcendental_Opi)),
    inference(rew,[status(thm),theory(equality)],[1273,162]),
    [iquote('0:Rew:1273.0,162.0')] ).

cnf(1304,plain,
    equal(c_Complex_Ocomplex_OComplex(u,c_Transcendental_Osin(c_Transcendental_Opi)),c_RealVector_Oof__real(u,tc_Complex_Ocomplex)),
    inference(rew,[status(thm),theory(equality)],[1274,1059]),
    [iquote('0:Rew:1274.0,1059.0')] ).

cnf(1323,plain,
    ~ equal(c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex)),
    inference(rew,[status(thm),theory(equality)],[1304,1264,1274]),
    [iquote('0:Rew:1304.0,1264.0,1274.0,1264.0')] ).

cnf(1497,plain,
    ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
    inference(res,[status(thm),theory(equality)],[1061,1323]),
    [iquote('0:Res:1061.1,1323.0')] ).

cnf(1543,plain,
    $false,
    inference(mrr,[status(thm)],[1497,1243]),
    [iquote('0:MRR:1497.0,1243.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWV573-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.13  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n027.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 : Thu Jun 16 05:45:35 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.47/0.71  
% 0.47/0.71  SPASS V 3.9 
% 0.47/0.71  SPASS beiseite: Proof found.
% 0.47/0.71  % SZS status Theorem
% 0.47/0.71  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.47/0.71  SPASS derived 27 clauses, backtracked 0 clauses, performed 0 splits and kept 1046 clauses.
% 0.47/0.71  SPASS allocated 77749 KBytes.
% 0.47/0.71  SPASS spent	0:00:00.35 on the problem.
% 0.47/0.71  		0:00:00.09 for the input.
% 0.47/0.71  		0:00:00.00 for the FLOTTER CNF translation.
% 0.47/0.71  		0:00:00.00 for inferences.
% 0.47/0.71  		0:00:00.00 for the backtracking.
% 0.47/0.71  		0:00:00.17 for the reduction.
% 0.47/0.71  
% 0.47/0.71  
% 0.47/0.71  Here is a proof with depth 1, length 15 :
% 0.47/0.71  % SZS output start Refutation
% See solution above
% 0.47/0.71  Formulae used in the proof : cls_complex__Re__i_0 cls_sin__pi_0 cls_tan__pi_0 cls_complex__of__real__def_0 cls_of__real__of__nat__eq_0 clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1 cls_conjecture_0
% 0.47/0.71  
%------------------------------------------------------------------------------