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
%------------------------------------------------------------------------------