TSTP Solution File: SWW208+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWW208+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 : Thu Jul 21 01:28:06 EDT 2022
% Result : Theorem 1.99s 2.19s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 22 ( 19 unt; 0 nHn; 22 RR)
% Number of literals : 28 ( 0 equ; 10 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(122,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('SWW208+1.p',unknown),
[] ).
cnf(232,axiom,
equal(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('SWW208+1.p',unknown),
[] ).
cnf(298,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
file('SWW208+1.p',unknown),
[] ).
cnf(316,axiom,
equal(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('SWW208+1.p',unknown),
[] ).
cnf(327,axiom,
equal(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Complex_Oii),
file('SWW208+1.p',unknown),
[] ).
cnf(329,axiom,
equal(c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(u,v)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('SWW208+1.p',unknown),
[] ).
cnf(396,axiom,
equal(c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,u),hAPP(c_Complex_OIm,u)),u),
file('SWW208+1.p',unknown),
[] ).
cnf(427,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(u)))),
file('SWW208+1.p',unknown),
[] ).
cnf(833,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,u)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
file('SWW208+1.p',unknown),
[] ).
cnf(1381,axiom,
( ~ class_Groups_Oordered__comm__monoid__add(u)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(u,v),w))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(u,c_Groups_Ozero__class_Ozero(u)),x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(u,v),hAPP(hAPP(c_Groups_Oplus__class_Oplus(u),x),w))) ),
file('SWW208+1.p',unknown),
[] ).
cnf(1577,axiom,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,skc8)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
file('SWW208+1.p',unknown),
[] ).
cnf(1800,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(mrr,[status(thm)],[1577,833]),
[iquote('0:MRR:1577.1,833.0')] ).
cnf(1851,plain,
( ~ class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(res,[status(thm),theory(equality)],[1381,1800]),
[iquote('0:Res:1381.3,1800.0')] ).
cnf(1864,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(mrr,[status(thm)],[1851,122,298]),
[iquote('0:MRR:1851.0,1851.1,122.0,298.0')] ).
cnf(1920,plain,
equal(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Complex_Ocomplex_Ocomplex__size(c_Complex_Oii)),
inference(spr,[status(thm),theory(equality)],[327,329]),
[iquote('0:SpR:327.0,329.0')] ).
cnf(1923,plain,
equal(c_Nat_OSuc(c_Complex_Ocomplex_Ocomplex__size(c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rew,[status(thm),theory(equality)],[1920,232]),
[iquote('0:Rew:1920.0,232.0')] ).
cnf(1930,plain,
equal(c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(u,v)),c_Complex_Ocomplex_Ocomplex__size(c_Complex_Oii)),
inference(rew,[status(thm),theory(equality)],[1920,329]),
[iquote('0:Rew:1920.0,329.0')] ).
cnf(2217,plain,
equal(c_Complex_Ocomplex_Ocomplex__size(u),c_Complex_Ocomplex_Ocomplex__size(c_Complex_Oii)),
inference(spr,[status(thm),theory(equality)],[396,1930]),
[iquote('0:SpR:396.0,1930.0')] ).
cnf(2252,plain,
equal(c_Nat_OSuc(c_Complex_Ocomplex_Ocomplex__size(u)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(spr,[status(thm),theory(equality)],[2217,1923]),
[iquote('0:SpR:2217.0,1923.0')] ).
cnf(2465,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(spr,[status(thm),theory(equality)],[2252,427]),
[iquote('0:SpR:2252.0,427.0')] ).
cnf(2467,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(rew,[status(thm),theory(equality)],[316,2465]),
[iquote('0:Rew:316.0,2465.0')] ).
cnf(2468,plain,
$false,
inference(mrr,[status(thm)],[2467,1864]),
[iquote('0:MRR:2467.0,1864.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWW208+1 : TPTP v8.1.0. Released v5.2.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jun 4 16:29:45 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.99/2.19
% 1.99/2.19 SPASS V 3.9
% 1.99/2.19 SPASS beiseite: Proof found.
% 1.99/2.19 % SZS status Theorem
% 1.99/2.19 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.99/2.19 SPASS derived 560 clauses, backtracked 0 clauses, performed 0 splits and kept 1696 clauses.
% 1.99/2.19 SPASS allocated 107781 KBytes.
% 1.99/2.19 SPASS spent 0:00:01.79 on the problem.
% 1.99/2.19 0:00:00.07 for the input.
% 1.99/2.19 0:00:00.59 for the FLOTTER CNF translation.
% 1.99/2.19 0:00:00.01 for inferences.
% 1.99/2.19 0:00:00.00 for the backtracking.
% 1.99/2.19 0:00:00.94 for the reduction.
% 1.99/2.19
% 1.99/2.19
% 1.99/2.19 Here is a proof with depth 3, length 22 :
% 1.99/2.19 % SZS output start Refutation
% See solution above
% 1.99/2.19 Formulae used in the proof : arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add fact_One__nat__def fact_rp fact_real__of__nat__1 fact_i__def fact_complex_Osize_I1_J fact_complex__surj fact_real__of__nat__Suc__gt__zero fact_th fact_add__strict__increasing2 conj_0
% 1.99/2.19
%------------------------------------------------------------------------------