TSTP Solution File: SWV603-1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWV603-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 21:44:32 EDT 2022

% Result   : Unsatisfiable 0.53s 0.73s
% Output   : Refutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   26 (  26 unt;   0 nHn;  26 RR)
%            Number of literals    :   26 (   0 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   23 (  23 usr;   8 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(142,axiom,
    equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Ouminus__class_Ouminus(v,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(u,v,tc_RealDef_Oreal)),
    file('SWV603-1.p',unknown),
    [] ).

cnf(336,axiom,
    equal(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(u,v,tc_RealDef_Oreal),v,tc_RealDef_Oreal),u),
    file('SWV603-1.p',unknown),
    [] ).

cnf(429,axiom,
    equal(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
    file('SWV603-1.p',unknown),
    [] ).

cnf(448,axiom,
    equal(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi)),
    file('SWV603-1.p',unknown),
    [] ).

cnf(474,axiom,
    equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
    file('SWV603-1.p',unknown),
    [] ).

cnf(555,axiom,
    equal(c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(u,u,tc_RealDef_Oreal)),c_HOL_Oabs__class_Oabs(u,tc_RealDef_Oreal)),
    file('SWV603-1.p',unknown),
    [] ).

cnf(707,axiom,
    equal(c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
    file('SWV603-1.p',unknown),
    [] ).

cnf(734,axiom,
    equal(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(u,v,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(w,v,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(u,w,tc_RealDef_Oreal),v,tc_RealDef_Oreal)),
    file('SWV603-1.p',unknown),
    [] ).

cnf(869,axiom,
    ~ equal(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),
    file('SWV603-1.p',unknown),
    [] ).

cnf(934,axiom,
    equal(c_HOL_Otimes__class_Otimes(u,v,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v,u,tc_RealDef_Oreal)),
    file('SWV603-1.p',unknown),
    [] ).

cnf(1110,axiom,
    equal(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
    file('SWV603-1.p',unknown),
    [] ).

cnf(1111,axiom,
    equal(c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),
    file('SWV603-1.p',unknown),
    [] ).

cnf(1117,plain,
    ~ equal(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi)),
    inference(rew,[status(thm),theory(equality)],[448,869]),
    [iquote('0:Rew:448.0,869.0')] ).

cnf(1120,plain,
    equal(c_NthRoot_Osqrt(c_Transcendental_Otan(c_Transcendental_Opi)),c_Transcendental_Otan(c_Transcendental_Opi)),
    inference(rew,[status(thm),theory(equality)],[448,707]),
    [iquote('0:Rew:448.0,707.0')] ).

cnf(1126,plain,
    equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi)),
    inference(rew,[status(thm),theory(equality)],[448,474]),
    [iquote('0:Rew:448.0,474.0')] ).

cnf(1146,plain,
    equal(c_HOL_Ominus__class_Ominus(u,u,tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi)),
    inference(rew,[status(thm),theory(equality)],[142,1126]),
    [iquote('0:Rew:142.0,1126.0')] ).

cnf(1204,plain,
    equal(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),c_Transcendental_Otan(c_Transcendental_Opi)),
    inference(rew,[status(thm),theory(equality)],[934,1110,448]),
    [iquote('0:Rew:934.0,1110.0,448.0,1110.0')] ).

cnf(1214,plain,
    equal(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi)),
    inference(rew,[status(thm),theory(equality)],[448,429]),
    [iquote('0:Rew:448.0,429.0')] ).

cnf(1219,plain,
    equal(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi)),
    inference(rew,[status(thm),theory(equality)],[734,1214]),
    [iquote('0:Rew:734.0,1214.0')] ).

cnf(1220,plain,
    equal(c_HOL_Otimes__class_Otimes(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Oplus__class_Oplus(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi)),
    inference(rew,[status(thm),theory(equality)],[934,1219]),
    [iquote('0:Rew:934.0,1219.0')] ).

cnf(1233,plain,
    equal(c_HOL_Oabs__class_Oabs(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(rew,[status(thm),theory(equality)],[1204,1111,934]),
    [iquote('0:Rew:1204.0,1111.0,934.0,1111.0')] ).

cnf(1455,plain,
    equal(c_HOL_Oplus__class_Oplus(c_Transcendental_Otan(c_Transcendental_Opi),u,tc_RealDef_Oreal),u),
    inference(spr,[status(thm),theory(equality)],[1146,336]),
    [iquote('0:SpR:1146.0,336.0')] ).

cnf(1457,plain,
    equal(c_HOL_Otimes__class_Otimes(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi)),
    inference(rew,[status(thm),theory(equality)],[1455,1220]),
    [iquote('0:Rew:1455.0,1220.0')] ).

cnf(1462,plain,
    equal(c_HOL_Oabs__class_Oabs(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Transcendental_Otan(c_Transcendental_Opi))),
    inference(spr,[status(thm),theory(equality)],[1457,555]),
    [iquote('0:SpR:1457.0,555.0')] ).

cnf(1464,plain,
    equal(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi)),
    inference(rew,[status(thm),theory(equality)],[1233,1462,1120]),
    [iquote('0:Rew:1233.0,1462.0,1120.0,1462.0')] ).

cnf(1465,plain,
    $false,
    inference(mrr,[status(thm)],[1464,1117]),
    [iquote('0:MRR:1464.0,1117.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWV603-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n020.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 : Tue Jun 14 17:55:34 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.53/0.73  
% 0.53/0.73  SPASS V 3.9 
% 0.53/0.73  SPASS beiseite: Proof found.
% 0.53/0.73  % SZS status Theorem
% 0.53/0.73  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.53/0.73  SPASS derived 137 clauses, backtracked 0 clauses, performed 0 splits and kept 965 clauses.
% 0.53/0.73  SPASS allocated 77728 KBytes.
% 0.53/0.73  SPASS spent	0:00:00.36 on the problem.
% 0.53/0.73  		0:00:00.09 for the input.
% 0.53/0.73  		0:00:00.00 for the FLOTTER CNF translation.
% 0.53/0.73  		0:00:00.00 for inferences.
% 0.53/0.73  		0:00:00.00 for the backtracking.
% 0.53/0.73  		0:00:00.19 for the reduction.
% 0.53/0.73  
% 0.53/0.73  
% 0.53/0.73  Here is a proof with depth 1, length 26 :
% 0.53/0.73  % SZS output start Refutation
% See solution above
% 0.53/0.73  Formulae used in the proof : cls_real__diff__def_0 cls_eq__diff__eq_H_0 cls_real__two__squares__add__zero__iff_2 cls_tan__pi_0 cls_real__add__eq__0__iff_1 cls_real__sqrt__abs2_0 cls_real__sqrt__zero_0 cls_real__add__mult__distrib_0 cls_real__zero__not__eq__one_0 cls_real__mult__commute_0 cls_conjecture_0 cls_conjecture_1
% 0.53/0.73  
%------------------------------------------------------------------------------