TSTP Solution File: SCT159+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SCT159+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 22:13:45 EDT 2022
% Result : Theorem 31.76s 31.99s
% Output : Refutation 31.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 22
% Syntax : Number of clauses : 50 ( 23 unt; 8 nHn; 50 RR)
% Number of literals : 82 ( 0 equ; 34 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 22 ( 22 usr; 10 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(36,axiom,
equal(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),
file('SCT159+1.p',unknown),
[] ).
cnf(40,axiom,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,u,u),
file('SCT159+1.p',unknown),
[] ).
cnf(42,axiom,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,u),
file('SCT159+1.p',unknown),
[] ).
cnf(44,axiom,
equal(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
file('SCT159+1.p',unknown),
[] ).
cnf(45,axiom,
equal(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fFalse)),
file('SCT159+1.p',unknown),
[] ).
cnf(47,axiom,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
file('SCT159+1.p',unknown),
[] ).
cnf(69,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,tc_HOL_Obool)),v)),
file('SCT159+1.p',unknown),
[] ).
cnf(107,axiom,
( skP0(u,v,w)
| c_member(w,v,u) ),
file('SCT159+1.p',unknown),
[] ).
cnf(126,axiom,
( ~ hBOOL(hAPP(u,v))
| c_member(w,v,u) ),
file('SCT159+1.p',unknown),
[] ).
cnf(132,axiom,
( equal(u,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),u) ),
file('SCT159+1.p',unknown),
[] ).
cnf(133,axiom,
c_Orderings_Oord__class_Oless__eq(tc_fun(u,tc_HOL_Obool),v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_HOL_Obool))),
file('SCT159+1.p',unknown),
[] ).
cnf(135,axiom,
( ~ equal(u,v)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,u,v) ),
file('SCT159+1.p',unknown),
[] ).
cnf(154,axiom,
~ equal(skf46(u,v,w),skf45(v,w,u)),
file('SCT159+1.p',unknown),
[] ).
cnf(155,axiom,
( ~ skP0(u,v,w)
| ~ c_member(w,v,u) ),
file('SCT159+1.p',unknown),
[] ).
cnf(207,axiom,
( ~ equal(hAPP(c_Nat_OSuc,u),hAPP(c_Nat_OSuc,v))
| equal(u,v) ),
file('SCT159+1.p',unknown),
[] ).
cnf(215,axiom,
( ~ equal(u,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,u,hAPP(c_Nat_OSuc,v)) ),
file('SCT159+1.p',unknown),
[] ).
cnf(259,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),u)
| equal(hAPP(c_Nat_OSuc,skf66(u)),u) ),
file('SCT159+1.p',unknown),
[] ).
cnf(309,axiom,
equal(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('SCT159+1.p',unknown),
[] ).
cnf(332,axiom,
( ~ c_Finite__Set_Ofinite(u,v)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(u,tc_HOL_Obool),w,v)
| c_Finite__Set_Ofinite(u,w) ),
file('SCT159+1.p',unknown),
[] ).
cnf(333,axiom,
( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,u)
| ~ c_member(tc_Nat_Onat,v,u)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,v,skf56(u)) ),
file('SCT159+1.p',unknown),
[] ).
cnf(468,axiom,
( ~ c_Finite__Set_Ofinite(u,c_Set_Oimage(v,u,w,x))
| ~ c_Fun_Oinj__on(v,u,w,x)
| c_Finite__Set_Ofinite(v,x) ),
file('SCT159+1.p',unknown),
[] ).
cnf(509,axiom,
( equal(hAPP(u,skf46(u,v,w)),hAPP(u,skf45(v,w,u)))
| c_Fun_Oinj__on(w,x,u,v) ),
file('SCT159+1.p',unknown),
[] ).
cnf(759,plain,
equal(c_HOL_Obool_Obool__size(c_fFalse),c_HOL_Obool_Obool__size(c_fTrue)),
inference(rew,[status(thm),theory(equality)],[45,44]),
[iquote('0:Rew:45.0,44.0')] ).
cnf(760,plain,
equal(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
inference(rew,[status(thm),theory(equality)],[759,45]),
[iquote('0:Rew:759.0,45.0')] ).
cnf(763,plain,
equal(c_Orderings_Obot__class_Obot(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
inference(rew,[status(thm),theory(equality)],[36,760]),
[iquote('0:Rew:36.0,760.0')] ).
cnf(764,plain,
equal(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
inference(rew,[status(thm),theory(equality)],[763,36]),
[iquote('0:Rew:763.0,36.0')] ).
cnf(782,plain,
( equal(u,c_HOL_Obool_Obool__size(c_fTrue))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue),u) ),
inference(rew,[status(thm),theory(equality)],[764,132]),
[iquote('0:Rew:764.0,132.1,764.0,132.0')] ).
cnf(792,plain,
( ~ equal(u,c_HOL_Obool_Obool__size(c_fTrue))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,u,hAPP(c_Nat_OSuc,v)) ),
inference(rew,[status(thm),theory(equality)],[764,215]),
[iquote('0:Rew:764.0,215.0')] ).
cnf(799,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue),u)
| equal(hAPP(c_Nat_OSuc,skf66(u)),u) ),
inference(rew,[status(thm),theory(equality)],[764,259]),
[iquote('0:Rew:764.0,259.0')] ).
cnf(802,plain,
equal(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue))),
inference(rew,[status(thm),theory(equality)],[764,309]),
[iquote('0:Rew:764.0,309.0')] ).
cnf(1641,plain,
( ~ hBOOL(hAPP(u,v))
| ~ skP0(u,v,w) ),
inference(res,[status(thm),theory(equality)],[126,155]),
[iquote('0:Res:126.1,155.1')] ).
cnf(1663,plain,
( ~ equal(u,c_HOL_Obool_Obool__size(c_fTrue))
| ~ equal(u,hAPP(c_Nat_OSuc,v)) ),
inference(res,[status(thm),theory(equality)],[792,135]),
[iquote('0:Res:792.1,135.1')] ).
cnf(1685,plain,
~ skP0(c_Orderings_Otop__class_Otop(tc_fun(u,tc_HOL_Obool)),v,w),
inference(res,[status(thm),theory(equality)],[69,1641]),
[iquote('0:Res:69.0,1641.0')] ).
cnf(4384,plain,
( equal(u,c_HOL_Obool_Obool__size(c_fTrue))
| equal(hAPP(c_Nat_OSuc,skf66(u)),u) ),
inference(res,[status(thm),theory(equality)],[782,799]),
[iquote('0:Res:782.1,799.0')] ).
cnf(5286,plain,
( ~ equal(u,hAPP(c_Nat_OSuc,v))
| equal(u,c_HOL_Obool_Obool__size(c_fTrue))
| equal(skf66(u),v) ),
inference(spl,[status(thm),theory(equality)],[4384,207]),
[iquote('0:SpL:4384.1,207.0')] ).
cnf(5304,plain,
( ~ equal(u,hAPP(c_Nat_OSuc,v))
| equal(skf66(u),v) ),
inference(mrr,[status(thm)],[5286,1663]),
[iquote('0:MRR:5286.1,1663.0')] ).
cnf(6664,plain,
equal(skf66(hAPP(c_Nat_OSuc,u)),u),
inference(eqr,[status(thm),theory(equality)],[5304]),
[iquote('0:EqR:5304.0')] ).
cnf(12978,plain,
( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,u)
| ~ c_member(tc_Nat_Onat,skf56(u),u) ),
inference(res,[status(thm),theory(equality)],[333,40]),
[iquote('0:Res:333.2,40.0')] ).
cnf(13043,plain,
( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,u)
| skP0(u,skf56(u),tc_Nat_Onat) ),
inference(res,[status(thm),theory(equality)],[107,12978]),
[iquote('0:Res:107.1,12978.1')] ).
cnf(13068,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(u,tc_HOL_Obool))),
inference(res,[status(thm),theory(equality)],[13043,1685]),
[iquote('0:Res:13043.1,1685.0')] ).
cnf(14301,plain,
( ~ c_Finite__Set_Ofinite(u,c_Orderings_Otop__class_Otop(tc_fun(u,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(u,v) ),
inference(res,[status(thm),theory(equality)],[133,332]),
[iquote('0:Res:133.0,332.1')] ).
cnf(14310,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,u),
inference(res,[status(thm),theory(equality)],[47,14301]),
[iquote('0:Res:47.0,14301.0')] ).
cnf(41505,plain,
( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue)))
| ~ c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(spl,[status(thm),theory(equality)],[802,468]),
[iquote('0:SpL:802.0,468.0')] ).
cnf(41511,plain,
( ~ c_Fun_Oinj__on(u,tc_Arrow__Order__Mirabelle_Oindi,v,w)
| c_Finite__Set_Ofinite(u,w) ),
inference(res,[status(thm),theory(equality)],[14310,468]),
[iquote('0:Res:14310.0,468.0')] ).
cnf(41534,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue))),
inference(mrr,[status(thm)],[41505,42,13068]),
[iquote('0:MRR:41505.1,41505.2,42.0,13068.0')] ).
cnf(50689,plain,
( c_Fun_Oinj__on(u,v,c_Nat_OSuc,w)
| equal(skf66(hAPP(c_Nat_OSuc,skf45(w,u,c_Nat_OSuc))),skf46(c_Nat_OSuc,w,u)) ),
inference(spr,[status(thm),theory(equality)],[509,6664]),
[iquote('0:SpR:509.0,6664.0')] ).
cnf(50929,plain,
( c_Fun_Oinj__on(u,v,c_Nat_OSuc,w)
| equal(skf46(c_Nat_OSuc,w,u),skf45(w,u,c_Nat_OSuc)) ),
inference(rew,[status(thm),theory(equality)],[6664,50689]),
[iquote('0:Rew:6664.0,50689.1')] ).
cnf(50930,plain,
c_Fun_Oinj__on(u,v,c_Nat_OSuc,w),
inference(mrr,[status(thm)],[50929,154]),
[iquote('0:MRR:50929.1,154.0')] ).
cnf(50932,plain,
c_Finite__Set_Ofinite(u,v),
inference(res,[status(thm),theory(equality)],[50930,41511]),
[iquote('0:Res:50930.0,41511.0')] ).
cnf(50936,plain,
$false,
inference(unc,[status(thm)],[50932,41534]),
[iquote('0:UnC:50932.0,41534.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SCT159+1 : TPTP v8.1.0. Released v5.2.0.
% 0.02/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n018.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 : Fri Jul 1 21:12:18 EDT 2022
% 0.11/0.33 % CPUTime :
% 31.76/31.99
% 31.76/31.99 SPASS V 3.9
% 31.76/31.99 SPASS beiseite: Proof found.
% 31.76/31.99 % SZS status Theorem
% 31.76/31.99 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.76/31.99 SPASS derived 40899 clauses, backtracked 0 clauses, performed 0 splits and kept 10934 clauses.
% 31.76/31.99 SPASS allocated 130251 KBytes.
% 31.76/31.99 SPASS spent 0:0:31.01 on the problem.
% 31.76/31.99 0:00:00.05 for the input.
% 31.76/31.99 0:00:00.59 for the FLOTTER CNF translation.
% 31.76/31.99 0:00:00.49 for inferences.
% 31.76/31.99 0:00:00.00 for the backtracking.
% 31.76/31.99 0:0:29.51 for the reduction.
% 31.76/31.99
% 31.76/31.99
% 31.76/31.99 Here is a proof with depth 5, length 50 :
% 31.76/31.99 % SZS output start Refutation
% See solution above
% 31.76/31.99 Formulae used in the proof : fact_bot__nat__def fact_less__not__refl3 fact_inj__Suc fact_bool_Osize_I1_J fact_bool_Osize_I2_J fact_finite__indi fact_top1I fact_equalityCE fact_mem__def fact_neq0__conv fact_subset__UNIV fact_nat__less__le fact_inj__on__def fact_le__eq__less__or__eq fact_Suc__n__not__le__n fact_Suc__inject fact_less__Suc__eq__0__disj fact_gr0__conv__Suc fact_greaterThan__0 fact_rev__finite__subset fact_finite__nat__set__iff__bounded arity_Nat__Onat__Orderings_Oorder fact_less__imp__neq fact_finite__imageD
% 31.76/31.99
%------------------------------------------------------------------------------