%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MSC010+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:28:15 PM UTC 2026
% Result : Theorem 0.02s 0.42s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 58
% Syntax : Number of formulae : 351 ( 36 unt; 56 def)
% Number of atoms : 1797 ( 242 equ)
% Maximal formula atoms : 68 ( 5 avg)
% Number of connectives : 2354 ( 908 ~; 955 |; 387 &)
% ( 56 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 60 ( 58 usr; 48 prp; 0-2 aty)
% Number of functors : 40 ( 40 usr; 38 con; 0-3 aty)
% Number of variables : 455 ( 413 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( ( ! [X19] :
( ( leq(X19,pred(pv63))
& leq(n0,X19) )
=> ! [X20] :
( ( leq(X20,n5)
& leq(n0,X20) )
=> a_select3(id_ds1_filter_init,X19,X20) = init ) )
& ! [X17,X18] :
( ( leq(X18,n5)
& leq(X17,n5)
& leq(n0,X18)
& leq(n0,X17) )
=> ( gt(pv63,X17)
=> a_select3(id_ds1_filter_init,X17,X18) = init ) )
& ! [X15,X16] :
( ( leq(X16,n5)
& leq(X15,n5)
& leq(n0,X16)
& leq(n0,X15) )
=> ( ( gt(pv64,X16)
& X15 = pv63 )
=> a_select3(id_ds1_filter_init,X15,X16) = init ) )
& ! [X13,X14] :
( ( leq(X14,n5)
& leq(X13,n5)
& leq(n0,X14)
& leq(n0,X13) )
=> a_select3(pminus_ds1_filter_init,X13,X14) = init )
& ! [X11,X12] :
( ( leq(X12,n0)
& leq(X11,n5)
& leq(n0,X12)
& leq(n0,X11) )
=> a_select3(xhatmin_ds1_filter_init,X11,X12) = init )
& ! [X9,X10] :
( ( leq(X10,n2)
& leq(X9,n2)
& leq(n0,X10)
& leq(n0,X9) )
=> a_select3(r_ds1_filter_init,X9,X10) = init )
& ! [X7,X8] :
( ( leq(X8,n5)
& leq(X7,n5)
& leq(n0,X8)
& leq(n0,X7) )
=> a_select3(q_ds1_filter_init,X7,X8) = init )
& ! [X5,X6] :
( ( leq(X6,n0)
& leq(X5,n5)
& leq(n0,X6)
& leq(n0,X5) )
=> a_select3(dv_ds1_filter_init,X5,X6) = init )
& ! [X3,X4] :
( ( leq(X4,n5)
& leq(X3,n5)
& leq(n0,X4)
& leq(n0,X3) )
=> a_select3(phi_ds1_filter_init,X3,X4) = init )
& ! [X1,X2] :
( ( leq(X2,n5)
& leq(X1,n2)
& leq(n0,X2)
& leq(n0,X1) )
=> a_select3(h_ds1_filter_init,X1,X2) = init )
& leq(pv64,n5)
& leq(pv63,n5)
& leq(pv5,n998)
& leq(n0,pv64)
& leq(n0,pv63)
& leq(n0,pv5)
& pv63 != pv64 )
=> ! [X21,X22] :
( ( leq(X22,n5)
& leq(X21,n5)
& leq(n0,X22)
& leq(n0,X21) )
=> ( ( leq(X22,pv64)
& X21 = pv63
& pv64 != X22 )
=> a_select3(id_ds1_filter_init,X21,X22) = init ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,conjecture,
~ ~ ( ( ! [X19] :
( ( leq(X19,pred(pv63))
& leq(n0,X19) )
=> ! [X20] :
( ( leq(X20,n5)
& leq(n0,X20) )
=> a_select3(id_ds1_filter_init,X19,X20) = init ) )
& ! [X17,X18] :
( ( leq(X18,n5)
& leq(X17,n5)
& leq(n0,X18)
& leq(n0,X17) )
=> ( gt(pv63,X17)
=> a_select3(id_ds1_filter_init,X17,X18) = init ) )
& ! [X15,X16] :
( ( leq(X16,n5)
& leq(X15,n5)
& leq(n0,X16)
& leq(n0,X15) )
=> ( ( gt(pv64,X16)
& X15 = pv63 )
=> a_select3(id_ds1_filter_init,X15,X16) = init ) )
& ! [X13,X14] :
( ( leq(X14,n5)
& leq(X13,n5)
& leq(n0,X14)
& leq(n0,X13) )
=> a_select3(pminus_ds1_filter_init,X13,X14) = init )
& ! [X11,X12] :
( ( leq(X12,n0)
& leq(X11,n5)
& leq(n0,X12)
& leq(n0,X11) )
=> a_select3(xhatmin_ds1_filter_init,X11,X12) = init )
& ! [X9,X10] :
( ( leq(X10,n2)
& leq(X9,n2)
& leq(n0,X10)
& leq(n0,X9) )
=> a_select3(r_ds1_filter_init,X9,X10) = init )
& ! [X7,X8] :
( ( leq(X8,n5)
& leq(X7,n5)
& leq(n0,X8)
& leq(n0,X7) )
=> a_select3(q_ds1_filter_init,X7,X8) = init )
& ! [X5,X6] :
( ( leq(X6,n0)
& leq(X5,n5)
& leq(n0,X6)
& leq(n0,X5) )
=> a_select3(dv_ds1_filter_init,X5,X6) = init )
& ! [X3,X4] :
( ( leq(X4,n5)
& leq(X3,n5)
& leq(n0,X4)
& leq(n0,X3) )
=> a_select3(phi_ds1_filter_init,X3,X4) = init )
& ! [X1,X2] :
( ( leq(X2,n5)
& leq(X1,n2)
& leq(n0,X2)
& leq(n0,X1) )
=> a_select3(h_ds1_filter_init,X1,X2) = init )
& leq(pv64,n5)
& leq(pv63,n5)
& leq(pv5,n998)
& leq(n0,pv64)
& leq(n0,pv63)
& leq(n0,pv5)
& pv63 != pv64 )
=> ! [X21,X22] :
( ( leq(X22,n5)
& leq(X21,n5)
& leq(n0,X22)
& leq(n0,X21) )
=> ( ( leq(X22,pv64)
& X21 = pv63
& pv64 != X22 )
=> a_select3(id_ds1_filter_init,X21,X22) = init ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ ~ ~ ( ( ! [X19] :
( ( leq(X19,pred(pv63))
& leq(n0,X19) )
=> ! [X20] :
( ( leq(X20,n5)
& leq(n0,X20) )
=> a_select3(id_ds1_filter_init,X19,X20) = init ) )
& ! [X17,X18] :
( ( leq(X18,n5)
& leq(X17,n5)
& leq(n0,X18)
& leq(n0,X17) )
=> ( gt(pv63,X17)
=> a_select3(id_ds1_filter_init,X17,X18) = init ) )
& ! [X15,X16] :
( ( leq(X16,n5)
& leq(X15,n5)
& leq(n0,X16)
& leq(n0,X15) )
=> ( ( gt(pv64,X16)
& X15 = pv63 )
=> a_select3(id_ds1_filter_init,X15,X16) = init ) )
& ! [X13,X14] :
( ( leq(X14,n5)
& leq(X13,n5)
& leq(n0,X14)
& leq(n0,X13) )
=> a_select3(pminus_ds1_filter_init,X13,X14) = init )
& ! [X11,X12] :
( ( leq(X12,n0)
& leq(X11,n5)
& leq(n0,X12)
& leq(n0,X11) )
=> a_select3(xhatmin_ds1_filter_init,X11,X12) = init )
& ! [X9,X10] :
( ( leq(X10,n2)
& leq(X9,n2)
& leq(n0,X10)
& leq(n0,X9) )
=> a_select3(r_ds1_filter_init,X9,X10) = init )
& ! [X7,X8] :
( ( leq(X8,n5)
& leq(X7,n5)
& leq(n0,X8)
& leq(n0,X7) )
=> a_select3(q_ds1_filter_init,X7,X8) = init )
& ! [X5,X6] :
( ( leq(X6,n0)
& leq(X5,n5)
& leq(n0,X6)
& leq(n0,X5) )
=> a_select3(dv_ds1_filter_init,X5,X6) = init )
& ! [X3,X4] :
( ( leq(X4,n5)
& leq(X3,n5)
& leq(n0,X4)
& leq(n0,X3) )
=> a_select3(phi_ds1_filter_init,X3,X4) = init )
& ! [X1,X2] :
( ( leq(X2,n5)
& leq(X1,n2)
& leq(n0,X2)
& leq(n0,X1) )
=> a_select3(h_ds1_filter_init,X1,X2) = init )
& leq(pv64,n5)
& leq(pv63,n5)
& leq(pv5,n998)
& leq(n0,pv64)
& leq(n0,pv63)
& leq(n0,pv5)
& pv63 != pv64 )
=> ! [X21,X22] :
( ( leq(X22,n5)
& leq(X21,n5)
& leq(n0,X22)
& leq(n0,X21) )
=> ( ( leq(X22,pv64)
& X21 = pv63
& pv64 != X22 )
=> a_select3(id_ds1_filter_init,X21,X22) = init ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
( ! [X21,X22] :
( a_select3(id_ds1_filter_init,X21,X22) = init
| ~ leq(X22,pv64)
| X21 != pv63
| pv64 = X22
| ~ leq(X22,n5)
| ~ leq(X21,n5)
| ~ leq(n0,X22)
| ~ leq(n0,X21) )
| ? [X19] :
( ? [X20] :
( a_select3(id_ds1_filter_init,X19,X20) != init
& leq(X20,n5)
& leq(n0,X20) )
& leq(X19,pred(pv63))
& leq(n0,X19) )
| ? [X17,X18] :
( a_select3(id_ds1_filter_init,X17,X18) != init
& gt(pv63,X17)
& leq(X18,n5)
& leq(X17,n5)
& leq(n0,X18)
& leq(n0,X17) )
| ? [X15,X16] :
( a_select3(id_ds1_filter_init,X15,X16) != init
& gt(pv64,X16)
& X15 = pv63
& leq(X16,n5)
& leq(X15,n5)
& leq(n0,X16)
& leq(n0,X15) )
| ? [X13,X14] :
( a_select3(pminus_ds1_filter_init,X13,X14) != init
& leq(X14,n5)
& leq(X13,n5)
& leq(n0,X14)
& leq(n0,X13) )
| ? [X11,X12] :
( a_select3(xhatmin_ds1_filter_init,X11,X12) != init
& leq(X12,n0)
& leq(X11,n5)
& leq(n0,X12)
& leq(n0,X11) )
| ? [X9,X10] :
( a_select3(r_ds1_filter_init,X9,X10) != init
& leq(X10,n2)
& leq(X9,n2)
& leq(n0,X10)
& leq(n0,X9) )
| ? [X7,X8] :
( a_select3(q_ds1_filter_init,X7,X8) != init
& leq(X8,n5)
& leq(X7,n5)
& leq(n0,X8)
& leq(n0,X7) )
| ? [X5,X6] :
( a_select3(dv_ds1_filter_init,X5,X6) != init
& leq(X6,n0)
& leq(X5,n5)
& leq(n0,X6)
& leq(n0,X5) )
| ? [X3,X4] :
( a_select3(phi_ds1_filter_init,X3,X4) != init
& leq(X4,n5)
& leq(X3,n5)
& leq(n0,X4)
& leq(n0,X3) )
| ? [X1,X2] :
( a_select3(h_ds1_filter_init,X1,X2) != init
& leq(X2,n5)
& leq(X1,n2)
& leq(n0,X2)
& leq(n0,X1) )
| ~ leq(pv64,n5)
| ~ leq(pv63,n5)
| ~ leq(pv5,n998)
| ~ leq(n0,pv64)
| ~ leq(n0,pv63)
| ~ leq(n0,pv5)
| pv63 = pv64 ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f5,definition,
! [X1,X2] :
( sP0_prd(X2,X1)
<=> ( a_select3(h_ds1_filter_init,X1,X2) != init
& leq(X2,n5)
& leq(X1,n2)
& leq(n0,X2)
& leq(n0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f6,definition,
! [X3,X4] :
( sP1_prd(X4,X3)
<=> ( a_select3(phi_ds1_filter_init,X3,X4) != init
& leq(X4,n5)
& leq(X3,n5)
& leq(n0,X4)
& leq(n0,X3) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f7,definition,
! [X5,X6] :
( sP2_prd(X6,X5)
<=> ( a_select3(dv_ds1_filter_init,X5,X6) != init
& leq(X6,n0)
& leq(X5,n5)
& leq(n0,X6)
& leq(n0,X5) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f8,definition,
! [X7,X8] :
( sP3_prd(X8,X7)
<=> ( a_select3(q_ds1_filter_init,X7,X8) != init
& leq(X8,n5)
& leq(X7,n5)
& leq(n0,X8)
& leq(n0,X7) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f9,definition,
! [X9,X10] :
( sP4_prd(X10,X9)
<=> ( a_select3(r_ds1_filter_init,X9,X10) != init
& leq(X10,n2)
& leq(X9,n2)
& leq(n0,X10)
& leq(n0,X9) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f10,definition,
! [X11,X12] :
( sP5_prd(X12,X11)
<=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) != init
& leq(X12,n0)
& leq(X11,n5)
& leq(n0,X12)
& leq(n0,X11) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f11,definition,
! [X13,X14] :
( sP6_prd(X14,X13)
<=> ( a_select3(pminus_ds1_filter_init,X13,X14) != init
& leq(X14,n5)
& leq(X13,n5)
& leq(n0,X14)
& leq(n0,X13) ) ),
introduced(definition,[new_symbols(definition,[sP6_prd])],[]) ).
fof(f12,definition,
! [X15,X16] :
( sP7_prd(X16,X15)
<=> ( a_select3(id_ds1_filter_init,X15,X16) != init
& gt(pv64,X16)
& X15 = pv63
& leq(X16,n5)
& leq(X15,n5)
& leq(n0,X16)
& leq(n0,X15) ) ),
introduced(definition,[new_symbols(definition,[sP7_prd])],[]) ).
fof(f13,definition,
! [X17,X18] :
( sP8_prd(X18,X17)
<=> ( a_select3(id_ds1_filter_init,X17,X18) != init
& gt(pv63,X17)
& leq(X18,n5)
& leq(X17,n5)
& leq(n0,X18)
& leq(n0,X17) ) ),
introduced(definition,[new_symbols(definition,[sP8_prd])],[]) ).
fof(f14,plain,
( ! [X21,X22] :
( a_select3(id_ds1_filter_init,X21,X22) = init
| ~ leq(X22,pv64)
| X21 != pv63
| pv64 = X22
| ~ leq(X22,n5)
| ~ leq(X21,n5)
| ~ leq(n0,X22)
| ~ leq(n0,X21) )
| ? [X19] :
( ? [X20] :
( a_select3(id_ds1_filter_init,X19,X20) != init
& leq(X20,n5)
& leq(n0,X20) )
& leq(X19,pred(pv63))
& leq(n0,X19) )
| ? [X17,X18] : sP8_prd(X18,X17)
| ? [X15,X16] : sP7_prd(X16,X15)
| ? [X13,X14] : sP6_prd(X14,X13)
| ? [X11,X12] : sP5_prd(X12,X11)
| ? [X9,X10] : sP4_prd(X10,X9)
| ? [X7,X8] : sP3_prd(X8,X7)
| ? [X5,X6] : sP2_prd(X6,X5)
| ? [X3,X4] : sP1_prd(X4,X3)
| ? [X1,X2] : sP0_prd(X2,X1)
| ~ leq(pv64,n5)
| ~ leq(pv63,n5)
| ~ leq(pv5,n998)
| ~ leq(n0,pv64)
| ~ leq(n0,pv63)
| ~ leq(n0,pv5)
| pv63 = pv64 ),
inference(formula_renaming,[status(thm)],[f4,f13,f12,f11,f10,f9,f8,f7,f6,f5]) ).
fof(f15,plain,
( ! [X21,X22] :
( a_select3(id_ds1_filter_init,X21,X22) = init
| ~ leq(X22,pv64)
| X21 != pv63
| pv64 = X22
| ~ leq(X22,n5)
| ~ leq(X21,n5)
| ~ leq(n0,X22)
| ~ leq(n0,X21) )
| ( a_select3(id_ds1_filter_init,sK18_skl,sK19_skl) != init
& leq(sK19_skl,n5)
& leq(n0,sK19_skl)
& leq(sK18_skl,pred(pv63))
& leq(n0,sK18_skl) )
| sP8_prd(sK17_skl,sK16_skl)
| sP7_prd(sK15_skl,sK14_skl)
| sP6_prd(sK13_skl,sK12_skl)
| sP5_prd(sK11_skl,sK10_skl)
| sP4_prd(sK9_skl,sK8_skl)
| sP3_prd(sK7_skl,sK6_skl)
| sP2_prd(sK5_skl,sK4_skl)
| sP1_prd(sK3_skl,sK2_skl)
| sP0_prd(sK1_skl,sK0_skl)
| ~ leq(pv64,n5)
| ~ leq(pv63,n5)
| ~ leq(pv5,n998)
| ~ leq(n0,pv64)
| ~ leq(n0,pv63)
| ~ leq(n0,pv5)
| pv63 = pv64 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl,sK8_skl,sK9_skl,sK10_skl,sK11_skl,sK12_skl,sK13_skl,sK14_skl,sK15_skl,sK16_skl,sK17_skl,sK18_skl,sK19_skl]),skolemize(X1,sK0_skl),skolemize(X2,sK1_skl),skolemize(X3,sK2_skl),skolemize(X4,sK3_skl),skolemize(X5,sK4_skl),skolemize(X6,sK5_skl),skolemize(X7,sK6_skl),skolemize(X8,sK7_skl),skolemize(X9,sK8_skl),skolemize(X10,sK9_skl),skolemize(X11,sK10_skl),skolemize(X12,sK11_skl),skolemize(X13,sK12_skl),skolemize(X14,sK13_skl),skolemize(X15,sK14_skl),skolemize(X16,sK15_skl),skolemize(X17,sK16_skl),skolemize(X18,sK17_skl),skolemize(X19,sK18_skl),skolemize(X20,sK19_skl)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( a_select3(id_ds1_filter_init,X0,X1) = init
| ~ leq(X1,pv64)
| X0 != pv63
| pv64 = X1
| ~ leq(X1,n5)
| ~ leq(X0,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X0)
| leq(n0,sK18_skl)
| sP8_prd(sK17_skl,sK16_skl)
| sP7_prd(sK15_skl,sK14_skl)
| sP6_prd(sK13_skl,sK12_skl)
| sP5_prd(sK11_skl,sK10_skl)
| sP4_prd(sK9_skl,sK8_skl)
| sP3_prd(sK7_skl,sK6_skl)
| sP2_prd(sK5_skl,sK4_skl)
| sP1_prd(sK3_skl,sK2_skl)
| sP0_prd(sK1_skl,sK0_skl)
| ~ leq(pv64,n5)
| ~ leq(pv63,n5)
| ~ leq(pv5,n998)
| ~ leq(n0,pv64)
| ~ leq(n0,pv63)
| ~ leq(n0,pv5)
| pv63 = pv64 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( a_select3(id_ds1_filter_init,X0,X1) = init
| ~ leq(X1,pv64)
| X0 != pv63
| pv64 = X1
| ~ leq(X1,n5)
| ~ leq(X0,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X0)
| leq(sK18_skl,pred(pv63))
| sP8_prd(sK17_skl,sK16_skl)
| sP7_prd(sK15_skl,sK14_skl)
| sP6_prd(sK13_skl,sK12_skl)
| sP5_prd(sK11_skl,sK10_skl)
| sP4_prd(sK9_skl,sK8_skl)
| sP3_prd(sK7_skl,sK6_skl)
| sP2_prd(sK5_skl,sK4_skl)
| sP1_prd(sK3_skl,sK2_skl)
| sP0_prd(sK1_skl,sK0_skl)
| ~ leq(pv64,n5)
| ~ leq(pv63,n5)
| ~ leq(pv5,n998)
| ~ leq(n0,pv64)
| ~ leq(n0,pv63)
| ~ leq(n0,pv5)
| pv63 = pv64 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,plain,
! [X0,X1] :
( a_select3(id_ds1_filter_init,X0,X1) = init
| ~ leq(X1,pv64)
| X0 != pv63
| pv64 = X1
| ~ leq(X1,n5)
| ~ leq(X0,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X0)
| leq(n0,sK19_skl)
| sP8_prd(sK17_skl,sK16_skl)
| sP7_prd(sK15_skl,sK14_skl)
| sP6_prd(sK13_skl,sK12_skl)
| sP5_prd(sK11_skl,sK10_skl)
| sP4_prd(sK9_skl,sK8_skl)
| sP3_prd(sK7_skl,sK6_skl)
| sP2_prd(sK5_skl,sK4_skl)
| sP1_prd(sK3_skl,sK2_skl)
| sP0_prd(sK1_skl,sK0_skl)
| ~ leq(pv64,n5)
| ~ leq(pv63,n5)
| ~ leq(pv5,n998)
| ~ leq(n0,pv64)
| ~ leq(n0,pv63)
| ~ leq(n0,pv5)
| pv63 = pv64 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f19,plain,
! [X0,X1] :
( a_select3(id_ds1_filter_init,X0,X1) = init
| ~ leq(X1,pv64)
| X0 != pv63
| pv64 = X1
| ~ leq(X1,n5)
| ~ leq(X0,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X0)
| leq(sK19_skl,n5)
| sP8_prd(sK17_skl,sK16_skl)
| sP7_prd(sK15_skl,sK14_skl)
| sP6_prd(sK13_skl,sK12_skl)
| sP5_prd(sK11_skl,sK10_skl)
| sP4_prd(sK9_skl,sK8_skl)
| sP3_prd(sK7_skl,sK6_skl)
| sP2_prd(sK5_skl,sK4_skl)
| sP1_prd(sK3_skl,sK2_skl)
| sP0_prd(sK1_skl,sK0_skl)
| ~ leq(pv64,n5)
| ~ leq(pv63,n5)
| ~ leq(pv5,n998)
| ~ leq(n0,pv64)
| ~ leq(n0,pv63)
| ~ leq(n0,pv5)
| pv63 = pv64 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f20,plain,
! [X0,X1] :
( a_select3(id_ds1_filter_init,X0,X1) = init
| ~ leq(X1,pv64)
| X0 != pv63
| pv64 = X1
| ~ leq(X1,n5)
| ~ leq(X0,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X0)
| a_select3(id_ds1_filter_init,sK18_skl,sK19_skl) != init
| sP8_prd(sK17_skl,sK16_skl)
| sP7_prd(sK15_skl,sK14_skl)
| sP6_prd(sK13_skl,sK12_skl)
| sP5_prd(sK11_skl,sK10_skl)
| sP4_prd(sK9_skl,sK8_skl)
| sP3_prd(sK7_skl,sK6_skl)
| sP2_prd(sK5_skl,sK4_skl)
| sP1_prd(sK3_skl,sK2_skl)
| sP0_prd(sK1_skl,sK0_skl)
| ~ leq(pv64,n5)
| ~ leq(pv63,n5)
| ~ leq(pv5,n998)
| ~ leq(n0,pv64)
| ~ leq(n0,pv63)
| ~ leq(n0,pv5)
| pv63 = pv64 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f21,plain,
( ? [X21,X22] :
( a_select3(id_ds1_filter_init,X21,X22) != init
& leq(X22,pv64)
& X21 = pv63
& pv64 != X22
& leq(X22,n5)
& leq(X21,n5)
& leq(n0,X22)
& leq(n0,X21) )
& ! [X19] :
( ! [X20] :
( a_select3(id_ds1_filter_init,X19,X20) = init
| ~ leq(X20,n5)
| ~ leq(n0,X20) )
| ~ leq(X19,pred(pv63))
| ~ leq(n0,X19) )
& ! [X17,X18] :
( a_select3(id_ds1_filter_init,X17,X18) = init
| ~ gt(pv63,X17)
| ~ leq(X18,n5)
| ~ leq(X17,n5)
| ~ leq(n0,X18)
| ~ leq(n0,X17) )
& ! [X15,X16] :
( a_select3(id_ds1_filter_init,X15,X16) = init
| ~ gt(pv64,X16)
| X15 != pv63
| ~ leq(X16,n5)
| ~ leq(X15,n5)
| ~ leq(n0,X16)
| ~ leq(n0,X15) )
& ! [X13,X14] :
( a_select3(pminus_ds1_filter_init,X13,X14) = init
| ~ leq(X14,n5)
| ~ leq(X13,n5)
| ~ leq(n0,X14)
| ~ leq(n0,X13) )
& ! [X11,X12] :
( a_select3(xhatmin_ds1_filter_init,X11,X12) = init
| ~ leq(X12,n0)
| ~ leq(X11,n5)
| ~ leq(n0,X12)
| ~ leq(n0,X11) )
& ! [X9,X10] :
( a_select3(r_ds1_filter_init,X9,X10) = init
| ~ leq(X10,n2)
| ~ leq(X9,n2)
| ~ leq(n0,X10)
| ~ leq(n0,X9) )
& ! [X7,X8] :
( a_select3(q_ds1_filter_init,X7,X8) = init
| ~ leq(X8,n5)
| ~ leq(X7,n5)
| ~ leq(n0,X8)
| ~ leq(n0,X7) )
& ! [X5,X6] :
( a_select3(dv_ds1_filter_init,X5,X6) = init
| ~ leq(X6,n0)
| ~ leq(X5,n5)
| ~ leq(n0,X6)
| ~ leq(n0,X5) )
& ! [X3,X4] :
( a_select3(phi_ds1_filter_init,X3,X4) = init
| ~ leq(X4,n5)
| ~ leq(X3,n5)
| ~ leq(n0,X4)
| ~ leq(n0,X3) )
& ! [X1,X2] :
( a_select3(h_ds1_filter_init,X1,X2) = init
| ~ leq(X2,n5)
| ~ leq(X1,n2)
| ~ leq(n0,X2)
| ~ leq(n0,X1) )
& leq(pv64,n5)
& leq(pv63,n5)
& leq(pv5,n998)
& leq(n0,pv64)
& leq(n0,pv63)
& leq(n0,pv5)
& pv63 != pv64 ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
( a_select3(id_ds1_filter_init,sK20_skl,sK21_skl) != init
& leq(sK21_skl,pv64)
& sK20_skl = pv63
& pv64 != sK21_skl
& leq(sK21_skl,n5)
& leq(sK20_skl,n5)
& leq(n0,sK21_skl)
& leq(n0,sK20_skl)
& ! [X19] :
( ! [X20] :
( a_select3(id_ds1_filter_init,X19,X20) = init
| ~ leq(X20,n5)
| ~ leq(n0,X20) )
| ~ leq(X19,pred(pv63))
| ~ leq(n0,X19) )
& ! [X17,X18] :
( a_select3(id_ds1_filter_init,X17,X18) = init
| ~ gt(pv63,X17)
| ~ leq(X18,n5)
| ~ leq(X17,n5)
| ~ leq(n0,X18)
| ~ leq(n0,X17) )
& ! [X15,X16] :
( a_select3(id_ds1_filter_init,X15,X16) = init
| ~ gt(pv64,X16)
| X15 != pv63
| ~ leq(X16,n5)
| ~ leq(X15,n5)
| ~ leq(n0,X16)
| ~ leq(n0,X15) )
& ! [X13,X14] :
( a_select3(pminus_ds1_filter_init,X13,X14) = init
| ~ leq(X14,n5)
| ~ leq(X13,n5)
| ~ leq(n0,X14)
| ~ leq(n0,X13) )
& ! [X11,X12] :
( a_select3(xhatmin_ds1_filter_init,X11,X12) = init
| ~ leq(X12,n0)
| ~ leq(X11,n5)
| ~ leq(n0,X12)
| ~ leq(n0,X11) )
& ! [X9,X10] :
( a_select3(r_ds1_filter_init,X9,X10) = init
| ~ leq(X10,n2)
| ~ leq(X9,n2)
| ~ leq(n0,X10)
| ~ leq(n0,X9) )
& ! [X7,X8] :
( a_select3(q_ds1_filter_init,X7,X8) = init
| ~ leq(X8,n5)
| ~ leq(X7,n5)
| ~ leq(n0,X8)
| ~ leq(n0,X7) )
& ! [X5,X6] :
( a_select3(dv_ds1_filter_init,X5,X6) = init
| ~ leq(X6,n0)
| ~ leq(X5,n5)
| ~ leq(n0,X6)
| ~ leq(n0,X5) )
& ! [X3,X4] :
( a_select3(phi_ds1_filter_init,X3,X4) = init
| ~ leq(X4,n5)
| ~ leq(X3,n5)
| ~ leq(n0,X4)
| ~ leq(n0,X3) )
& ! [X1,X2] :
( a_select3(h_ds1_filter_init,X1,X2) = init
| ~ leq(X2,n5)
| ~ leq(X1,n2)
| ~ leq(n0,X2)
| ~ leq(n0,X1) )
& leq(pv64,n5)
& leq(pv63,n5)
& leq(pv5,n998)
& leq(n0,pv64)
& leq(n0,pv63)
& leq(n0,pv5)
& pv63 != pv64 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl]),skolemize(X21,sK20_skl),skolemize(X22,sK21_skl)],[f21]) ).
fof(f23,plain,
pv63 != pv64,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
leq(n0,pv5),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
leq(n0,pv63),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f26,plain,
leq(n0,pv64),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f27,plain,
leq(pv5,n998),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f28,plain,
leq(pv63,n5),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f29,plain,
leq(pv64,n5),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f30,plain,
! [X0,X1] :
( a_select3(h_ds1_filter_init,X0,X1) = init
| ~ leq(X1,n5)
| ~ leq(X0,n2)
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f31,plain,
! [X0,X1] :
( a_select3(phi_ds1_filter_init,X0,X1) = init
| ~ leq(X1,n5)
| ~ leq(X0,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f32,plain,
! [X0,X1] :
( a_select3(dv_ds1_filter_init,X0,X1) = init
| ~ leq(X1,n0)
| ~ leq(X0,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f33,plain,
! [X0,X1] :
( a_select3(q_ds1_filter_init,X0,X1) = init
| ~ leq(X1,n5)
| ~ leq(X0,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f34,plain,
! [X0,X1] :
( a_select3(r_ds1_filter_init,X0,X1) = init
| ~ leq(X1,n2)
| ~ leq(X0,n2)
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f35,plain,
! [X0,X1] :
( a_select3(xhatmin_ds1_filter_init,X0,X1) = init
| ~ leq(X1,n0)
| ~ leq(X0,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f36,plain,
! [X0,X1] :
( a_select3(pminus_ds1_filter_init,X0,X1) = init
| ~ leq(X1,n5)
| ~ leq(X0,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f37,plain,
! [X0,X1] :
( a_select3(id_ds1_filter_init,X0,X1) = init
| ~ gt(pv64,X1)
| X0 != pv63
| ~ leq(X1,n5)
| ~ leq(X0,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f38,plain,
! [X0,X1] :
( a_select3(id_ds1_filter_init,X0,X1) = init
| ~ gt(pv63,X0)
| ~ leq(X1,n5)
| ~ leq(X0,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f39,plain,
! [X0,X1] :
( a_select3(id_ds1_filter_init,X0,X1) = init
| ~ leq(X1,n5)
| ~ leq(n0,X1)
| ~ leq(X0,pred(pv63))
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f41,plain,
leq(n0,sK21_skl),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f43,plain,
leq(sK21_skl,n5),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f44,plain,
pv64 != sK21_skl,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f45,plain,
sK20_skl = pv63,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f46,plain,
leq(sK21_skl,pv64),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f47,plain,
a_select3(id_ds1_filter_init,sK20_skl,sK21_skl) != init,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f48,plain,
! [X1,X2] :
( ( a_select3(h_ds1_filter_init,X1,X2) = init
| ~ leq(X2,n5)
| ~ leq(X1,n2)
| ~ leq(n0,X2)
| ~ leq(n0,X1)
| sP0_prd(X2,X1) )
& ( ( a_select3(h_ds1_filter_init,X1,X2) != init
& leq(X2,n5)
& leq(X1,n2)
& leq(n0,X2)
& leq(n0,X1) )
| ~ sP0_prd(X2,X1) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f49,plain,
( ! [X1,X2] :
( a_select3(h_ds1_filter_init,X1,X2) = init
| ~ leq(X2,n5)
| ~ leq(X1,n2)
| ~ leq(n0,X2)
| ~ leq(n0,X1)
| sP0_prd(X2,X1) )
& ! [X1,X2] :
( ( a_select3(h_ds1_filter_init,X1,X2) != init
& leq(X2,n5)
& leq(X1,n2)
& leq(n0,X2)
& leq(n0,X1) )
| ~ sP0_prd(X2,X1) ) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
! [X0,X1] :
( leq(X1,n2)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
! [X0,X1] :
( leq(X0,n5)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f54,plain,
! [X0,X1] :
( a_select3(h_ds1_filter_init,X1,X0) != init
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f56,plain,
! [X3,X4] :
( ( a_select3(phi_ds1_filter_init,X3,X4) = init
| ~ leq(X4,n5)
| ~ leq(X3,n5)
| ~ leq(n0,X4)
| ~ leq(n0,X3)
| sP1_prd(X4,X3) )
& ( ( a_select3(phi_ds1_filter_init,X3,X4) != init
& leq(X4,n5)
& leq(X3,n5)
& leq(n0,X4)
& leq(n0,X3) )
| ~ sP1_prd(X4,X3) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f57,plain,
( ! [X3,X4] :
( a_select3(phi_ds1_filter_init,X3,X4) = init
| ~ leq(X4,n5)
| ~ leq(X3,n5)
| ~ leq(n0,X4)
| ~ leq(n0,X3)
| sP1_prd(X4,X3) )
& ! [X3,X4] :
( ( a_select3(phi_ds1_filter_init,X3,X4) != init
& leq(X4,n5)
& leq(X3,n5)
& leq(n0,X4)
& leq(n0,X3) )
| ~ sP1_prd(X4,X3) ) ),
inference(miniscoping,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f60,plain,
! [X0,X1] :
( leq(X1,n5)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f61,plain,
! [X0,X1] :
( leq(X0,n5)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f62,plain,
! [X0,X1] :
( a_select3(phi_ds1_filter_init,X1,X0) != init
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f64,plain,
! [X5,X6] :
( ( a_select3(dv_ds1_filter_init,X5,X6) = init
| ~ leq(X6,n0)
| ~ leq(X5,n5)
| ~ leq(n0,X6)
| ~ leq(n0,X5)
| sP2_prd(X6,X5) )
& ( ( a_select3(dv_ds1_filter_init,X5,X6) != init
& leq(X6,n0)
& leq(X5,n5)
& leq(n0,X6)
& leq(n0,X5) )
| ~ sP2_prd(X6,X5) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f65,plain,
( ! [X5,X6] :
( a_select3(dv_ds1_filter_init,X5,X6) = init
| ~ leq(X6,n0)
| ~ leq(X5,n5)
| ~ leq(n0,X6)
| ~ leq(n0,X5)
| sP2_prd(X6,X5) )
& ! [X5,X6] :
( ( a_select3(dv_ds1_filter_init,X5,X6) != init
& leq(X6,n0)
& leq(X5,n5)
& leq(n0,X6)
& leq(n0,X5) )
| ~ sP2_prd(X6,X5) ) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
! [X0,X1] :
( leq(X1,n5)
| ~ sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f69,plain,
! [X0,X1] :
( leq(X0,n0)
| ~ sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f70,plain,
! [X0,X1] :
( a_select3(dv_ds1_filter_init,X1,X0) != init
| ~ sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f72,plain,
! [X7,X8] :
( ( a_select3(q_ds1_filter_init,X7,X8) = init
| ~ leq(X8,n5)
| ~ leq(X7,n5)
| ~ leq(n0,X8)
| ~ leq(n0,X7)
| sP3_prd(X8,X7) )
& ( ( a_select3(q_ds1_filter_init,X7,X8) != init
& leq(X8,n5)
& leq(X7,n5)
& leq(n0,X8)
& leq(n0,X7) )
| ~ sP3_prd(X8,X7) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f73,plain,
( ! [X7,X8] :
( a_select3(q_ds1_filter_init,X7,X8) = init
| ~ leq(X8,n5)
| ~ leq(X7,n5)
| ~ leq(n0,X8)
| ~ leq(n0,X7)
| sP3_prd(X8,X7) )
& ! [X7,X8] :
( ( a_select3(q_ds1_filter_init,X7,X8) != init
& leq(X8,n5)
& leq(X7,n5)
& leq(n0,X8)
& leq(n0,X7) )
| ~ sP3_prd(X8,X7) ) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f76,plain,
! [X0,X1] :
( leq(X1,n5)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f77,plain,
! [X0,X1] :
( leq(X0,n5)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f78,plain,
! [X0,X1] :
( a_select3(q_ds1_filter_init,X1,X0) != init
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f80,plain,
! [X9,X10] :
( ( a_select3(r_ds1_filter_init,X9,X10) = init
| ~ leq(X10,n2)
| ~ leq(X9,n2)
| ~ leq(n0,X10)
| ~ leq(n0,X9)
| sP4_prd(X10,X9) )
& ( ( a_select3(r_ds1_filter_init,X9,X10) != init
& leq(X10,n2)
& leq(X9,n2)
& leq(n0,X10)
& leq(n0,X9) )
| ~ sP4_prd(X10,X9) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f81,plain,
( ! [X9,X10] :
( a_select3(r_ds1_filter_init,X9,X10) = init
| ~ leq(X10,n2)
| ~ leq(X9,n2)
| ~ leq(n0,X10)
| ~ leq(n0,X9)
| sP4_prd(X10,X9) )
& ! [X9,X10] :
( ( a_select3(r_ds1_filter_init,X9,X10) != init
& leq(X10,n2)
& leq(X9,n2)
& leq(n0,X10)
& leq(n0,X9) )
| ~ sP4_prd(X10,X9) ) ),
inference(miniscoping,[status(thm)],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f84,plain,
! [X0,X1] :
( leq(X1,n2)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f85,plain,
! [X0,X1] :
( leq(X0,n2)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f86,plain,
! [X0,X1] :
( a_select3(r_ds1_filter_init,X1,X0) != init
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f88,plain,
! [X11,X12] :
( ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init
| ~ leq(X12,n0)
| ~ leq(X11,n5)
| ~ leq(n0,X12)
| ~ leq(n0,X11)
| sP5_prd(X12,X11) )
& ( ( a_select3(xhatmin_ds1_filter_init,X11,X12) != init
& leq(X12,n0)
& leq(X11,n5)
& leq(n0,X12)
& leq(n0,X11) )
| ~ sP5_prd(X12,X11) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f89,plain,
( ! [X11,X12] :
( a_select3(xhatmin_ds1_filter_init,X11,X12) = init
| ~ leq(X12,n0)
| ~ leq(X11,n5)
| ~ leq(n0,X12)
| ~ leq(n0,X11)
| sP5_prd(X12,X11) )
& ! [X11,X12] :
( ( a_select3(xhatmin_ds1_filter_init,X11,X12) != init
& leq(X12,n0)
& leq(X11,n5)
& leq(n0,X12)
& leq(n0,X11) )
| ~ sP5_prd(X12,X11) ) ),
inference(miniscoping,[status(thm)],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f92,plain,
! [X0,X1] :
( leq(X1,n5)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f93,plain,
! [X0,X1] :
( leq(X0,n0)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f94,plain,
! [X0,X1] :
( a_select3(xhatmin_ds1_filter_init,X1,X0) != init
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f96,plain,
! [X13,X14] :
( ( a_select3(pminus_ds1_filter_init,X13,X14) = init
| ~ leq(X14,n5)
| ~ leq(X13,n5)
| ~ leq(n0,X14)
| ~ leq(n0,X13)
| sP6_prd(X14,X13) )
& ( ( a_select3(pminus_ds1_filter_init,X13,X14) != init
& leq(X14,n5)
& leq(X13,n5)
& leq(n0,X14)
& leq(n0,X13) )
| ~ sP6_prd(X14,X13) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f97,plain,
( ! [X13,X14] :
( a_select3(pminus_ds1_filter_init,X13,X14) = init
| ~ leq(X14,n5)
| ~ leq(X13,n5)
| ~ leq(n0,X14)
| ~ leq(n0,X13)
| sP6_prd(X14,X13) )
& ! [X13,X14] :
( ( a_select3(pminus_ds1_filter_init,X13,X14) != init
& leq(X14,n5)
& leq(X13,n5)
& leq(n0,X14)
& leq(n0,X13) )
| ~ sP6_prd(X14,X13) ) ),
inference(miniscoping,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP6_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP6_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f100,plain,
! [X0,X1] :
( leq(X1,n5)
| ~ sP6_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f101,plain,
! [X0,X1] :
( leq(X0,n5)
| ~ sP6_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f102,plain,
! [X0,X1] :
( a_select3(pminus_ds1_filter_init,X1,X0) != init
| ~ sP6_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f104,plain,
! [X15,X16] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init
| ~ gt(pv64,X16)
| X15 != pv63
| ~ leq(X16,n5)
| ~ leq(X15,n5)
| ~ leq(n0,X16)
| ~ leq(n0,X15)
| sP7_prd(X16,X15) )
& ( ( a_select3(id_ds1_filter_init,X15,X16) != init
& gt(pv64,X16)
& X15 = pv63
& leq(X16,n5)
& leq(X15,n5)
& leq(n0,X16)
& leq(n0,X15) )
| ~ sP7_prd(X16,X15) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f105,plain,
( ! [X15,X16] :
( a_select3(id_ds1_filter_init,X15,X16) = init
| ~ gt(pv64,X16)
| X15 != pv63
| ~ leq(X16,n5)
| ~ leq(X15,n5)
| ~ leq(n0,X16)
| ~ leq(n0,X15)
| sP7_prd(X16,X15) )
& ! [X15,X16] :
( ( a_select3(id_ds1_filter_init,X15,X16) != init
& gt(pv64,X16)
& X15 = pv63
& leq(X16,n5)
& leq(X15,n5)
& leq(n0,X16)
& leq(n0,X15) )
| ~ sP7_prd(X16,X15) ) ),
inference(miniscoping,[status(thm)],[f104]) ).
fof(f107,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP7_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f109,plain,
! [X0,X1] :
( leq(X0,n5)
| ~ sP7_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f110,plain,
! [X0,X1] :
( X1 = pv63
| ~ sP7_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f111,plain,
! [X0,X1] :
( gt(pv64,X0)
| ~ sP7_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f112,plain,
! [X0,X1] :
( a_select3(id_ds1_filter_init,X1,X0) != init
| ~ sP7_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f114,plain,
! [X17,X18] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init
| ~ gt(pv63,X17)
| ~ leq(X18,n5)
| ~ leq(X17,n5)
| ~ leq(n0,X18)
| ~ leq(n0,X17)
| sP8_prd(X18,X17) )
& ( ( a_select3(id_ds1_filter_init,X17,X18) != init
& gt(pv63,X17)
& leq(X18,n5)
& leq(X17,n5)
& leq(n0,X18)
& leq(n0,X17) )
| ~ sP8_prd(X18,X17) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f115,plain,
( ! [X17,X18] :
( a_select3(id_ds1_filter_init,X17,X18) = init
| ~ gt(pv63,X17)
| ~ leq(X18,n5)
| ~ leq(X17,n5)
| ~ leq(n0,X18)
| ~ leq(n0,X17)
| sP8_prd(X18,X17) )
& ! [X17,X18] :
( ( a_select3(id_ds1_filter_init,X17,X18) != init
& gt(pv63,X17)
& leq(X18,n5)
& leq(X17,n5)
& leq(n0,X18)
& leq(n0,X17) )
| ~ sP8_prd(X18,X17) ) ),
inference(miniscoping,[status(thm)],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP8_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP8_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f118,plain,
! [X0,X1] :
( leq(X1,n5)
| ~ sP8_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f119,plain,
! [X0,X1] :
( leq(X0,n5)
| ~ sP8_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f120,plain,
! [X0,X1] :
( gt(pv63,X1)
| ~ sP8_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f121,plain,
! [X0,X1] :
( a_select3(id_ds1_filter_init,X1,X0) != init
| ~ sP8_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f123,definition,
( sQ0_spl
<=> pv63 = pv64 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f124,plain,
( ~ sQ0_spl
| pv63 = pv64 ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,definition,
( sQ1_spl
<=> leq(n0,pv5) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( sQ1_spl
| ~ leq(n0,pv5) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,definition,
( sQ2_spl
<=> leq(n0,pv63) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( sQ2_spl
| ~ leq(n0,pv63) ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,definition,
( sQ3_spl
<=> leq(n0,pv64) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( sQ3_spl
| ~ leq(n0,pv64) ),
inference(component_clause,[status(thm)],[f132]) ).
fof(f135,definition,
( sQ4_spl
<=> leq(pv5,n998) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( sQ4_spl
| ~ leq(pv5,n998) ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,definition,
( sQ5_spl
<=> leq(pv63,n5) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( sQ5_spl
| ~ leq(pv63,n5) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,definition,
( sQ6_spl
<=> leq(pv64,n5) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f143,plain,
( sQ6_spl
| ~ leq(pv64,n5) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,definition,
( sQ7_spl
<=> sP0_prd(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( ~ sQ7_spl
| sP0_prd(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,definition,
( sQ8_spl
<=> sP1_prd(sK3_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( ~ sQ8_spl
| sP1_prd(sK3_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,definition,
( sQ9_spl
<=> sP2_prd(sK5_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( ~ sQ9_spl
| sP2_prd(sK5_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,definition,
( sQ10_spl
<=> sP3_prd(sK7_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ10_spl
| sP3_prd(sK7_skl,sK6_skl) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,definition,
( sQ11_spl
<=> sP4_prd(sK9_skl,sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( ~ sQ11_spl
| sP4_prd(sK9_skl,sK8_skl) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,definition,
( sQ12_spl
<=> sP5_prd(sK11_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( ~ sQ12_spl
| sP5_prd(sK11_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,definition,
( sQ13_spl
<=> sP6_prd(sK13_skl,sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f163,plain,
( ~ sQ13_spl
| sP6_prd(sK13_skl,sK12_skl) ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f165,definition,
( sQ14_spl
<=> sP7_prd(sK15_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ14_spl
| sP7_prd(sK15_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,definition,
( sQ15_spl
<=> sP8_prd(sK17_skl,sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( ~ sQ15_spl
| sP8_prd(sK17_skl,sK16_skl) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,definition,
( sQ16_spl
<=> leq(n0,sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( ~ sQ16_spl
| leq(n0,sK18_skl) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,definition,
! [X0,X1] :
( sQ17_spl
<=> ( a_select3(id_ds1_filter_init,X0,X1) = init
| ~ leq(X1,pv64)
| X0 != pv63
| pv64 = X1
| ~ leq(X1,n5)
| ~ leq(X0,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f175,plain,
! [X0,X1] :
( ~ sQ17_spl
| a_select3(id_ds1_filter_init,X0,X1) = init
| ~ leq(X1,pv64)
| X0 != pv63
| pv64 = X1
| ~ leq(X1,n5)
| ~ leq(X0,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( sQ17_spl
| sQ16_spl
| sQ15_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl
| sQ10_spl
| sQ9_spl
| sQ8_spl
| sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f16,f123,f126,f129,f132,f135,f138,f141,f144,f147,f150,f153,f156,f159,f162,f165,f168,f171,f174]) ).
fof(f178,definition,
( sQ18_spl
<=> leq(sK18_skl,pred(pv63)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f179,plain,
( ~ sQ18_spl
| leq(sK18_skl,pred(pv63)) ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,plain,
( sQ17_spl
| sQ18_spl
| sQ15_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl
| sQ10_spl
| sQ9_spl
| sQ8_spl
| sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f17,f123,f126,f129,f132,f135,f138,f141,f144,f147,f150,f153,f156,f159,f162,f165,f168,f178,f174]) ).
fof(f182,definition,
( sQ19_spl
<=> leq(n0,sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( sQ17_spl
| sQ19_spl
| sQ15_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl
| sQ10_spl
| sQ9_spl
| sQ8_spl
| sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f18,f123,f126,f129,f132,f135,f138,f141,f144,f147,f150,f153,f156,f159,f162,f165,f168,f182,f174]) ).
fof(f186,definition,
( sQ20_spl
<=> leq(sK19_skl,n5) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( sQ17_spl
| sQ20_spl
| sQ15_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl
| sQ10_spl
| sQ9_spl
| sQ8_spl
| sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f19,f123,f126,f129,f132,f135,f138,f141,f144,f147,f150,f153,f156,f159,f162,f165,f168,f186,f174]) ).
fof(f190,definition,
( sQ21_spl
<=> a_select3(id_ds1_filter_init,sK18_skl,sK19_skl) = init ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( sQ21_spl
| a_select3(id_ds1_filter_init,sK18_skl,sK19_skl) != init ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,plain,
( sQ17_spl
| ~ sQ21_spl
| sQ15_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl
| sQ10_spl
| sQ9_spl
| sQ8_spl
| sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f20,f123,f126,f129,f132,f135,f138,f141,f144,f147,f150,f153,f156,f159,f162,f165,f168,f190,f174]) ).
fof(f194,plain,
! [X0] :
( a_select3(id_ds1_filter_init,pv63,X0) = init
| ~ gt(pv64,X0)
| ~ leq(X0,n5)
| ~ leq(pv63,n5)
| ~ leq(n0,X0)
| ~ leq(n0,pv63) ),
inference(destructive_equality_resolution,[status(thm)],[f37]) ).
fof(f196,plain,
! [X0] :
( ~ sQ17_spl
| a_select3(id_ds1_filter_init,pv63,X0) = init
| ~ leq(X0,pv64)
| pv64 = X0
| ~ leq(X0,n5)
| ~ leq(pv63,n5)
| ~ leq(n0,X0)
| ~ leq(n0,pv63) ),
inference(destructive_equality_resolution,[status(thm)],[f175]) ).
fof(f197,plain,
sK20_skl != pv64,
inference(backward_demodulation,[status(thm)],[f45,f23]) ).
fof(f198,plain,
leq(n0,sK20_skl),
inference(forward_demodulation,[status(thm)],[f45,f25]) ).
fof(f199,plain,
leq(sK20_skl,n5),
inference(forward_demodulation,[status(thm)],[f45,f28]) ).
fof(f200,plain,
! [X0,X1] :
( X1 = sK20_skl
| ~ sP7_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f45,f110]) ).
fof(f201,plain,
! [X0,X1] :
( a_select3(id_ds1_filter_init,X0,X1) = init
| ~ leq(X1,n5)
| ~ leq(n0,X1)
| ~ leq(X0,pred(sK20_skl))
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f45,f39]) ).
fof(f202,plain,
( ~ leq(sK21_skl,n5)
| ~ leq(n0,sK21_skl)
| ~ leq(sK20_skl,pred(sK20_skl))
| ~ leq(n0,sK20_skl) ),
inference(resolution,[status(thm)],[f201,f47]) ).
fof(f203,definition,
( sQ22_spl
<=> leq(n0,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( sQ22_spl
| ~ leq(n0,sK20_skl) ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f206,definition,
( sQ23_spl
<=> leq(sK20_skl,pred(sK20_skl)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f209,definition,
( sQ24_spl
<=> leq(n0,sK21_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f211,plain,
( sQ24_spl
| ~ leq(n0,sK21_skl) ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,definition,
( sQ25_spl
<=> leq(sK21_skl,n5) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( sQ25_spl
| ~ leq(sK21_skl,n5) ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f215,plain,
( ~ sQ25_spl
| ~ sQ24_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f202,f203,f206,f209,f212]) ).
fof(f216,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f143,f29]) ).
fof(f217,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f216]) ).
fof(f218,plain,
( sQ5_spl
| ~ leq(sK20_skl,n5) ),
inference(forward_demodulation,[status(thm)],[f45,f140]) ).
fof(f219,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f218,f199]) ).
fof(f220,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f219]) ).
fof(f221,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f137,f27]) ).
fof(f222,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f221]) ).
fof(f223,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f134,f26]) ).
fof(f224,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f223]) ).
fof(f225,plain,
( sQ2_spl
| ~ leq(n0,sK20_skl) ),
inference(forward_demodulation,[status(thm)],[f45,f131]) ).
fof(f226,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f225,f198]) ).
fof(f227,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f226]) ).
fof(f228,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f24]) ).
fof(f229,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f228]) ).
fof(f230,plain,
( ~ sQ0_spl
| sK20_skl = pv64 ),
inference(forward_demodulation,[status(thm)],[f45,f124]) ).
fof(f231,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f230,f197]) ).
fof(f232,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f231]) ).
fof(f233,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f214,f43]) ).
fof(f234,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f233]) ).
fof(f238,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f211,f41]) ).
fof(f239,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f240,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f205,f198]) ).
fof(f241,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f240]) ).
fof(f242,plain,
! [X0] :
( a_select3(id_ds1_filter_init,pv63,X0) = init
| ~ gt(pv64,X0)
| ~ leq(X0,n5)
| ~ leq(pv63,n5)
| ~ leq(n0,X0)
| ~ leq(n0,sK20_skl) ),
inference(forward_demodulation,[status(thm)],[f45,f194]) ).
fof(f243,plain,
! [X0] :
( a_select3(id_ds1_filter_init,pv63,X0) = init
| ~ gt(pv64,X0)
| ~ leq(X0,n5)
| ~ leq(sK20_skl,n5)
| ~ leq(n0,X0)
| ~ leq(n0,sK20_skl) ),
inference(forward_demodulation,[status(thm)],[f45,f242]) ).
fof(f244,plain,
! [X0] :
( a_select3(id_ds1_filter_init,sK20_skl,X0) = init
| ~ gt(pv64,X0)
| ~ leq(X0,n5)
| ~ leq(sK20_skl,n5)
| ~ leq(n0,X0)
| ~ leq(n0,sK20_skl) ),
inference(forward_demodulation,[status(thm)],[f45,f243]) ).
fof(f245,plain,
! [X0] :
( a_select3(id_ds1_filter_init,sK20_skl,X0) = init
| ~ gt(pv64,X0)
| ~ leq(X0,n5)
| ~ leq(sK20_skl,n5)
| ~ leq(n0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f244,f198]) ).
fof(f246,plain,
( ~ gt(pv64,sK21_skl)
| ~ leq(sK21_skl,n5)
| ~ leq(sK20_skl,n5)
| ~ leq(n0,sK21_skl) ),
inference(resolution,[status(thm)],[f245,f47]) ).
fof(f247,definition,
( sQ26_spl
<=> leq(sK20_skl,n5) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f249,plain,
( sQ26_spl
| ~ leq(sK20_skl,n5) ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,definition,
( sQ27_spl
<=> gt(pv64,sK21_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f253,plain,
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ26_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f246,f209,f247,f212,f250]) ).
fof(f254,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f249,f199]) ).
fof(f255,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f254]) ).
fof(f256,plain,
! [X0,X1] :
( gt(sK20_skl,X1)
| ~ sP8_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f45,f120]) ).
fof(f257,plain,
! [X0,X1] :
( ~ leq(X0,n5)
| ~ leq(X1,n2)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ sP0_prd(X0,X1) ),
inference(resolution,[status(thm)],[f54,f30]) ).
fof(f258,plain,
! [X0,X1] :
( ~ leq(X0,n5)
| ~ leq(X1,n2)
| ~ leq(n0,X1)
| ~ sP0_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f257,f51]) ).
fof(f259,plain,
! [X0,X1] :
( ~ leq(X0,n5)
| ~ leq(X1,n5)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ sP1_prd(X0,X1) ),
inference(resolution,[status(thm)],[f62,f31]) ).
fof(f260,plain,
! [X0,X1] :
( ~ leq(X0,n5)
| ~ leq(X1,n5)
| ~ leq(n0,X1)
| ~ sP1_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f59]) ).
fof(f261,plain,
! [X0,X1] :
( ~ leq(X0,n0)
| ~ leq(X1,n5)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ sP2_prd(X0,X1) ),
inference(resolution,[status(thm)],[f70,f32]) ).
fof(f262,plain,
! [X0,X1] :
( ~ leq(X0,n0)
| ~ leq(X1,n5)
| ~ leq(n0,X1)
| ~ sP2_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f261,f67]) ).
fof(f263,plain,
! [X0,X1] :
( ~ leq(X0,n5)
| ~ leq(X1,n5)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ sP3_prd(X0,X1) ),
inference(resolution,[status(thm)],[f78,f33]) ).
fof(f264,plain,
! [X0,X1] :
( ~ leq(X0,n5)
| ~ leq(X1,n5)
| ~ leq(n0,X1)
| ~ sP3_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f263,f75]) ).
fof(f265,plain,
! [X0,X1] :
( ~ leq(X0,n2)
| ~ leq(X1,n2)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ sP4_prd(X0,X1) ),
inference(resolution,[status(thm)],[f86,f34]) ).
fof(f266,plain,
! [X0,X1] :
( ~ leq(X1,n2)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ sP4_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f265,f85]) ).
fof(f267,plain,
! [X0,X1] :
( a_select3(id_ds1_filter_init,X0,X1) = init
| ~ gt(sK20_skl,X0)
| ~ leq(X1,n5)
| ~ leq(X0,n5)
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f45,f38]) ).
fof(f268,plain,
( ~ gt(sK20_skl,sK20_skl)
| ~ leq(sK21_skl,n5)
| ~ leq(sK20_skl,n5)
| ~ leq(n0,sK21_skl)
| ~ leq(n0,sK20_skl) ),
inference(resolution,[status(thm)],[f267,f47]) ).
fof(f269,definition,
( sQ28_spl
<=> gt(sK20_skl,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f272,plain,
( ~ sQ28_spl
| ~ sQ25_spl
| ~ sQ26_spl
| ~ sQ24_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f268,f203,f209,f247,f212,f269]) ).
fof(f273,plain,
! [X0,X1] :
( ~ leq(X0,n5)
| ~ leq(X1,n2)
| ~ sP0_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f258,f50]) ).
fof(f280,plain,
! [X0,X1] :
( ~ leq(X0,n5)
| ~ leq(X1,n5)
| ~ sP1_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f260,f58]) ).
fof(f298,plain,
! [X0,X1] :
( ~ leq(X0,n0)
| ~ leq(X1,n5)
| ~ sP2_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f262,f66]) ).
fof(f305,plain,
! [X0,X1] :
( ~ leq(X0,n0)
| ~ leq(X1,n5)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ sP5_prd(X0,X1) ),
inference(resolution,[status(thm)],[f94,f35]) ).
fof(f306,plain,
! [X0,X1] :
( ~ leq(X0,n0)
| ~ leq(X1,n5)
| ~ leq(n0,X1)
| ~ sP5_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f305,f91]) ).
fof(f307,plain,
! [X0,X1] :
( ~ leq(X0,n5)
| ~ leq(X1,n5)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ sP6_prd(X0,X1) ),
inference(resolution,[status(thm)],[f102,f36]) ).
fof(f308,plain,
! [X0,X1] :
( ~ leq(X0,n5)
| ~ leq(X1,n5)
| ~ leq(n0,X1)
| ~ sP6_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f307,f99]) ).
fof(f309,plain,
! [X0] :
( ~ gt(pv64,X0)
| ~ leq(X0,n5)
| ~ leq(sK20_skl,n5)
| ~ leq(n0,X0)
| ~ sP7_prd(X0,sK20_skl) ),
inference(resolution,[status(thm)],[f112,f245]) ).
fof(f312,definition,
! [X0] :
( sQ29_spl
<=> ( ~ gt(pv64,X0)
| ~ leq(X0,n5)
| ~ leq(n0,X0)
| ~ sP7_prd(X0,sK20_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f313,plain,
! [X0] :
( ~ sQ29_spl
| ~ gt(pv64,X0)
| ~ leq(X0,n5)
| ~ leq(n0,X0)
| ~ sP7_prd(X0,sK20_skl) ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f315,plain,
( ~ sQ26_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f309,f312,f247]) ).
fof(f318,plain,
! [X0] :
( ~ sQ29_spl
| ~ gt(pv64,X0)
| ~ leq(X0,n5)
| ~ sP7_prd(X0,sK20_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f313,f107]) ).
fof(f319,plain,
! [X0] :
( ~ gt(pv64,X0)
| ~ leq(X0,n5)
| ~ leq(sK20_skl,n5)
| ~ leq(n0,X0)
| ~ sP8_prd(X0,sK20_skl) ),
inference(resolution,[status(thm)],[f121,f245]) ).
fof(f320,plain,
! [X0,X1] :
( ~ gt(sK20_skl,X1)
| ~ leq(X0,n5)
| ~ leq(X1,n5)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ sP8_prd(X0,X1) ),
inference(resolution,[status(thm)],[f121,f267]) ).
fof(f322,definition,
! [X0] :
( sQ30_spl
<=> ( ~ gt(pv64,X0)
| ~ leq(X0,n5)
| ~ leq(n0,X0)
| ~ sP8_prd(X0,sK20_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f325,plain,
( ~ sQ26_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f319,f322,f247]) ).
fof(f326,plain,
! [X0,X1] :
( ~ gt(sK20_skl,X1)
| ~ leq(X0,n5)
| ~ leq(X1,n5)
| ~ leq(n0,X1)
| ~ sP8_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f320,f117]) ).
fof(f329,plain,
! [X0] :
( ~ sQ29_spl
| ~ gt(pv64,X0)
| ~ sP7_prd(X0,sK20_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f318,f109]) ).
fof(f331,plain,
! [X0,X1] :
( ~ leq(X0,n5)
| ~ leq(X1,n5)
| ~ sP3_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f264,f74]) ).
fof(f353,plain,
! [X0,X1] :
( ~ leq(X1,n2)
| ~ leq(n0,X1)
| ~ sP4_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f266,f83]) ).
fof(f386,plain,
! [X0,X1] :
( ~ leq(X0,n0)
| ~ leq(X1,n5)
| ~ sP5_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f306,f90]) ).
fof(f394,plain,
! [X0,X1] :
( ~ leq(X0,n5)
| ~ leq(X1,n5)
| ~ sP6_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f308,f98]) ).
fof(f459,plain,
! [X0] :
( ~ sQ17_spl
| a_select3(id_ds1_filter_init,pv63,X0) = init
| ~ leq(X0,pv64)
| pv64 = X0
| ~ leq(X0,n5)
| ~ leq(pv63,n5)
| ~ leq(n0,X0)
| ~ leq(n0,sK20_skl) ),
inference(forward_demodulation,[status(thm)],[f45,f196]) ).
fof(f460,plain,
! [X0] :
( ~ sQ17_spl
| a_select3(id_ds1_filter_init,pv63,X0) = init
| ~ leq(X0,pv64)
| pv64 = X0
| ~ leq(X0,n5)
| ~ leq(sK20_skl,n5)
| ~ leq(n0,X0)
| ~ leq(n0,sK20_skl) ),
inference(forward_demodulation,[status(thm)],[f45,f459]) ).
fof(f461,plain,
! [X0] :
( ~ sQ17_spl
| a_select3(id_ds1_filter_init,sK20_skl,X0) = init
| ~ leq(X0,pv64)
| pv64 = X0
| ~ leq(X0,n5)
| ~ leq(sK20_skl,n5)
| ~ leq(n0,X0)
| ~ leq(n0,sK20_skl) ),
inference(forward_demodulation,[status(thm)],[f45,f460]) ).
fof(f462,plain,
! [X0] :
( ~ sQ17_spl
| a_select3(id_ds1_filter_init,sK20_skl,X0) = init
| ~ leq(X0,pv64)
| pv64 = X0
| ~ leq(X0,n5)
| ~ leq(sK20_skl,n5)
| ~ leq(n0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f461,f198]) ).
fof(f463,plain,
( ~ sQ17_spl
| ~ leq(sK21_skl,pv64)
| pv64 = sK21_skl
| ~ leq(sK21_skl,n5)
| ~ leq(sK20_skl,n5)
| ~ leq(n0,sK21_skl) ),
inference(resolution,[status(thm)],[f462,f47]) ).
fof(f466,definition,
( sQ47_spl
<=> pv64 = sK21_skl ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( ~ sQ47_spl
| pv64 = sK21_skl ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,definition,
( sQ48_spl
<=> leq(sK21_skl,pv64) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( sQ48_spl
| ~ leq(sK21_skl,pv64) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f472,plain,
( ~ sQ17_spl
| ~ sQ48_spl
| sQ47_spl
| ~ sQ25_spl
| ~ sQ26_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f463,f209,f247,f212,f466,f469,f174]) ).
fof(f477,definition,
! [X0] :
( sQ50_spl
<=> ( ~ sP7_prd(X0,sK20_skl)
| ~ leq(X0,pv64)
| pv64 = X0
| ~ leq(X0,n5)
| ~ leq(n0,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f478,plain,
! [X0] :
( ~ sQ50_spl
| ~ sP7_prd(X0,sK20_skl)
| ~ leq(X0,pv64)
| pv64 = X0
| ~ leq(X0,n5)
| ~ leq(n0,X0) ),
inference(component_clause,[status(thm)],[f477]) ).
fof(f482,plain,
( ~ sQ15_spl
| leq(sK16_skl,n5) ),
inference(resolution,[status(thm)],[f169,f118]) ).
fof(f485,plain,
( ~ sQ15_spl
| gt(sK20_skl,sK16_skl) ),
inference(resolution,[status(thm)],[f169,f256]) ).
fof(f486,plain,
! [X0,X1] :
( ~ gt(sK20_skl,X1)
| ~ leq(X0,n5)
| ~ leq(X1,n5)
| ~ sP8_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f326,f116]) ).
fof(f525,plain,
! [X0] :
( ~ sQ15_spl
| ~ leq(X0,n5)
| ~ leq(sK16_skl,n5)
| ~ sP8_prd(X0,sK16_skl) ),
inference(resolution,[status(thm)],[f485,f486]) ).
fof(f527,definition,
! [X0] :
( sQ57_spl
<=> ( ~ leq(X0,n5)
| ~ sP8_prd(X0,sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f528,plain,
! [X0] :
( ~ sQ57_spl
| ~ leq(X0,n5)
| ~ sP8_prd(X0,sK16_skl) ),
inference(component_clause,[status(thm)],[f527]) ).
fof(f530,definition,
( sQ58_spl
<=> leq(sK16_skl,n5) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f532,plain,
( sQ58_spl
| ~ leq(sK16_skl,n5) ),
inference(component_clause,[status(thm)],[f530]) ).
fof(f533,plain,
( ~ sQ15_spl
| ~ sQ58_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f525,f527,f530,f168]) ).
fof(f547,plain,
( ~ sQ14_spl
| sK14_skl = sK20_skl ),
inference(resolution,[status(thm)],[f166,f200]) ).
fof(f548,plain,
( ~ sQ14_spl
| sP7_prd(sK15_skl,sK20_skl) ),
inference(backward_demodulation,[status(thm)],[f547,f166]) ).
fof(f612,plain,
( ~ sQ13_spl
| leq(sK13_skl,n5) ),
inference(resolution,[status(thm)],[f163,f101]) ).
fof(f616,plain,
( ~ sQ12_spl
| leq(sK11_skl,n0) ),
inference(resolution,[status(thm)],[f160,f93]) ).
fof(f621,plain,
( ~ sQ11_spl
| leq(n0,sK8_skl) ),
inference(resolution,[status(thm)],[f157,f82]) ).
fof(f623,plain,
( ~ sQ11_spl
| leq(sK8_skl,n2) ),
inference(resolution,[status(thm)],[f157,f84]) ).
fof(f624,plain,
( ~ sQ10_spl
| leq(sK7_skl,n5) ),
inference(resolution,[status(thm)],[f154,f77]) ).
fof(f628,plain,
( ~ sQ9_spl
| leq(sK5_skl,n0) ),
inference(resolution,[status(thm)],[f151,f69]) ).
fof(f632,plain,
( ~ sQ8_spl
| leq(sK3_skl,n5) ),
inference(resolution,[status(thm)],[f148,f61]) ).
fof(f639,plain,
( ~ sQ7_spl
| leq(sK0_skl,n2) ),
inference(resolution,[status(thm)],[f145,f52]) ).
fof(f649,plain,
! [X0] :
( ~ sQ13_spl
| ~ leq(X0,n5)
| ~ sP6_prd(sK13_skl,X0) ),
inference(resolution,[status(thm)],[f612,f394]) ).
fof(f686,plain,
! [X0] :
( ~ sQ13_spl
| ~ sP6_prd(sK13_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f649,f100]) ).
fof(f695,plain,
! [X0] :
( ~ sQ12_spl
| ~ leq(X0,n5)
| ~ sP5_prd(sK11_skl,X0) ),
inference(resolution,[status(thm)],[f616,f386]) ).
fof(f697,plain,
! [X0] :
( ~ sQ12_spl
| ~ sP5_prd(sK11_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f695,f92]) ).
fof(f699,plain,
( ~ sQ12_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f160,f697]) ).
fof(f700,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f699]) ).
fof(f723,plain,
! [X0] :
( ~ sQ10_spl
| ~ leq(X0,n5)
| ~ sP3_prd(sK7_skl,X0) ),
inference(resolution,[status(thm)],[f624,f331]) ).
fof(f758,plain,
! [X0] :
( ~ sQ10_spl
| ~ sP3_prd(sK7_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f723,f76]) ).
fof(f767,plain,
! [X0] :
( ~ sQ9_spl
| ~ leq(X0,n5)
| ~ sP2_prd(sK5_skl,X0) ),
inference(resolution,[status(thm)],[f628,f298]) ).
fof(f769,plain,
! [X0] :
( ~ sQ9_spl
| ~ sP2_prd(sK5_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f767,f68]) ).
fof(f846,plain,
! [X0] :
( ~ sQ8_spl
| ~ leq(X0,n5)
| ~ sP1_prd(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f632,f280]) ).
fof(f879,plain,
! [X0] :
( ~ sQ8_spl
| ~ sP1_prd(sK3_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f846,f60]) ).
fof(f885,plain,
! [X0] :
( ~ sQ7_spl
| ~ leq(X0,n5)
| ~ sP0_prd(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f639,f273]) ).
fof(f893,plain,
! [X0] :
( ~ sQ7_spl
| ~ sP0_prd(X0,sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f885,f53]) ).
fof(f899,plain,
! [X0] :
( ~ sQ57_spl
| ~ sP8_prd(X0,sK16_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f528,f119]) ).
fof(f903,plain,
! [X0] :
( ~ sQ50_spl
| ~ sP7_prd(X0,sK20_skl)
| ~ leq(X0,pv64)
| pv64 = X0
| ~ leq(X0,n5) ),
inference(forward_subsumption_resolution,[status(thm)],[f478,f107]) ).
fof(f905,plain,
( sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f471,f46]) ).
fof(f906,plain,
sQ48_spl,
inference(contradiction_clause,[status(thm)],[f905]) ).
fof(f907,plain,
( ~ sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f467,f44]) ).
fof(f908,plain,
~ sQ47_spl,
inference(contradiction_clause,[status(thm)],[f907]) ).
fof(f912,plain,
( ~ sQ18_spl
| leq(sK18_skl,pred(sK20_skl)) ),
inference(forward_demodulation,[status(thm)],[f45,f179]) ).
fof(f917,plain,
! [X0] :
( ~ sQ50_spl
| ~ sP7_prd(X0,sK20_skl)
| ~ leq(X0,pv64)
| pv64 = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[f903,f109]) ).
fof(f918,plain,
( ~ sQ50_spl
| ~ sP7_prd(sK21_skl,sK20_skl)
| pv64 = sK21_skl ),
inference(resolution,[status(thm)],[f917,f46]) ).
fof(f919,plain,
( ~ sQ50_spl
| ~ sP7_prd(n0,sK20_skl)
| pv64 = n0 ),
inference(resolution,[status(thm)],[f917,f26]) ).
fof(f920,definition,
( sQ89_spl
<=> sP7_prd(sK21_skl,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f923,plain,
( ~ sQ50_spl
| ~ sQ89_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f918,f466,f920,f477]) ).
fof(f924,definition,
( sQ90_spl
<=> pv64 = n0 ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f925,plain,
( ~ sQ90_spl
| pv64 = n0 ),
inference(component_clause,[status(thm)],[f924]) ).
fof(f927,definition,
( sQ91_spl
<=> sP7_prd(n0,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f930,plain,
( ~ sQ50_spl
| ~ sQ91_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f919,f924,f927,f477]) ).
fof(f947,plain,
! [X0] :
( ~ sQ90_spl
| a_select3(id_ds1_filter_init,sK20_skl,X0) = init
| ~ gt(n0,X0)
| ~ leq(X0,n5)
| ~ leq(sK20_skl,n5)
| ~ leq(n0,X0) ),
inference(backward_demodulation,[status(thm)],[f925,f245]) ).
fof(f953,definition,
! [X0] :
( sQ92_spl
<=> ( a_select3(id_ds1_filter_init,sK20_skl,X0) = init
| ~ gt(n0,X0)
| ~ leq(X0,n5)
| ~ leq(n0,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f954,plain,
! [X0] :
( ~ sQ92_spl
| a_select3(id_ds1_filter_init,sK20_skl,X0) = init
| ~ gt(n0,X0)
| ~ leq(X0,n5)
| ~ leq(n0,X0) ),
inference(component_clause,[status(thm)],[f953]) ).
fof(f956,plain,
( ~ sQ90_spl
| ~ sQ26_spl
| sQ92_spl ),
inference(split_clause,[status(thm)],[f947,f953,f247,f924]) ).
fof(f957,definition,
! [X0] :
( sQ93_spl
<=> ( a_select3(id_ds1_filter_init,sK20_skl,X0) = init
| ~ gt(pv64,X0)
| ~ leq(X0,n5)
| ~ leq(n0,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f960,plain,
( ~ sQ26_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f245,f957,f247]) ).
fof(f962,plain,
( sQ21_spl
| ~ leq(sK19_skl,n5)
| ~ leq(n0,sK19_skl)
| ~ leq(sK18_skl,pred(sK20_skl))
| ~ leq(n0,sK18_skl) ),
inference(resolution,[status(thm)],[f192,f201]) ).
fof(f970,definition,
( sQ96_spl
<=> leq(sK18_skl,pred(sK20_skl)) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f972,plain,
( sQ96_spl
| ~ leq(sK18_skl,pred(sK20_skl)) ),
inference(component_clause,[status(thm)],[f970]) ).
fof(f973,plain,
( sQ21_spl
| ~ sQ20_spl
| ~ sQ19_spl
| ~ sQ96_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f962,f171,f970,f182,f186,f190]) ).
fof(f974,plain,
( sQ96_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f972,f912]) ).
fof(f975,plain,
( sQ96_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f974]) ).
fof(f978,plain,
( ~ sQ15_spl
| ~ sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f169,f899]) ).
fof(f979,plain,
( ~ sQ15_spl
| ~ sQ57_spl ),
inference(contradiction_clause,[status(thm)],[f978]) ).
fof(f981,plain,
( ~ sQ92_spl
| ~ gt(n0,sK21_skl)
| ~ leq(sK21_skl,n5)
| ~ leq(n0,sK21_skl) ),
inference(resolution,[status(thm)],[f954,f47]) ).
fof(f984,definition,
( sQ97_spl
<=> gt(n0,sK21_skl) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f987,plain,
( ~ sQ92_spl
| ~ sQ97_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f981,f209,f212,f984,f953]) ).
fof(f1020,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f145,f893]) ).
fof(f1021,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f1020]) ).
fof(f1050,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f148,f879]) ).
fof(f1051,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f1050]) ).
fof(f1057,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f769]) ).
fof(f1058,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f1057]) ).
fof(f1060,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f154,f758]) ).
fof(f1061,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f1060]) ).
fof(f1063,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f163,f686]) ).
fof(f1064,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f1063]) ).
fof(f1068,plain,
! [X0] :
( ~ sQ29_spl
| ~ sP7_prd(X0,sK20_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f329,f111]) ).
fof(f1071,plain,
! [X0] :
( ~ sQ16_spl
| ~ leq(sK18_skl,n2)
| ~ sP4_prd(X0,sK18_skl) ),
inference(resolution,[status(thm)],[f172,f353]) ).
fof(f1072,definition,
! [X0] :
( sQ101_spl
<=> ~ sP4_prd(X0,sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1075,definition,
( sQ102_spl
<=> leq(sK18_skl,n2) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1078,plain,
( ~ sQ16_spl
| ~ sQ102_spl
| sQ101_spl ),
inference(split_clause,[status(thm)],[f1071,f1072,f1075,f171]) ).
fof(f1085,plain,
( ~ sQ14_spl
| ~ sQ29_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f548,f1068]) ).
fof(f1086,plain,
( ~ sQ14_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f1085]) ).
fof(f1089,definition,
! [X0] :
( sQ103_spl
<=> ~ sP4_prd(X0,sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1090,plain,
! [X0] :
( ~ sQ103_spl
| ~ sP4_prd(X0,sK8_skl) ),
inference(component_clause,[status(thm)],[f1089]) ).
fof(f1106,plain,
( ~ sQ11_spl
| ~ sQ103_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f1090]) ).
fof(f1107,plain,
( ~ sQ11_spl
| ~ sQ103_spl ),
inference(contradiction_clause,[status(thm)],[f1106]) ).
fof(f1108,plain,
! [X0] :
( ~ sQ11_spl
| ~ leq(sK8_skl,n2)
| ~ sP4_prd(X0,sK8_skl) ),
inference(resolution,[status(thm)],[f621,f353]) ).
fof(f1109,definition,
( sQ106_spl
<=> leq(sK8_skl,n2) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1111,plain,
( sQ106_spl
| ~ leq(sK8_skl,n2) ),
inference(component_clause,[status(thm)],[f1109]) ).
fof(f1112,plain,
( ~ sQ11_spl
| ~ sQ106_spl
| sQ103_spl ),
inference(split_clause,[status(thm)],[f1108,f1089,f1109,f156]) ).
fof(f1113,plain,
( sQ106_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1111,f623]) ).
fof(f1114,plain,
( sQ106_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1113]) ).
fof(f1115,plain,
( ~ sQ15_spl
| sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f482,f532]) ).
fof(f1116,plain,
( ~ sQ15_spl
| sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f1115]) ).
fof(f1117,plain,
$false,
inference(sat_refutation,[status(thm)],[f177,f181,f185,f189,f193,f215,f217,f220,f222,f224,f227,f229,f232,f234,f239,f241,f253,f255,f272,f315,f325,f472,f533,f700,f906,f908,f923,f930,f956,f960,f973,f975,f979,f987,f1021,f1051,f1058,f1061,f1064,f1078,f1086,f1107,f1112,f1114,f1116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MSC010+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 01:29:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.02/0.39 % Drodi V4.1.1
% 0.02/0.42 % Refutation found
% 0.02/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.02/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.02/0.44 % Elapsed time: 0.061508 seconds
% 0.02/0.44 % CPU time: 0.233478 seconds
% 0.02/0.44 % Total memory used: 88.072 MB
% 0.02/0.44 % Net memory used: 87.855 MB
%------------------------------------------------------------------------------