TSTP Solution File: SWV050+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV050+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n012.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 : 300s
% DateTime : Tue Apr 30 16:37:23 EDT 2024
% Result : Theorem 0.20s 0.42s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 281
% Syntax : Number of formulae : 864 ( 262 unt; 0 def)
% Number of atoms : 2244 ( 397 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 2222 ( 842 ~; 827 |; 328 &)
% ( 189 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 203 ( 201 usr; 187 prp; 0-4 aty)
% Number of functors : 61 ( 61 usr; 21 con; 0-4 aty)
% Number of variables : 1059 ( 961 !; 98 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2047,plain,
$false,
inference(avatar_sat_refutation,[],[f451,f456,f461,f466,f471,f476,f481,f486,f491,f496,f501,f506,f511,f516,f521,f526,f531,f536,f541,f546,f551,f556,f560,f564,f569,f574,f578,f583,f588,f593,f598,f608,f614,f625,f630,f635,f639,f672,f678,f684,f689,f693,f698,f702,f706,f727,f733,f738,f743,f748,f753,f757,f762,f766,f771,f775,f780,f784,f789,f793,f798,f803,f807,f811,f816,f820,f825,f829,f834,f838,f843,f847,f853,f857,f861,f866,f870,f875,f879,f884,f888,f893,f897,f903,f907,f911,f916,f920,f925,f929,f934,f938,f943,f947,f953,f957,f962,f966,f971,f975,f980,f984,f988,f992,f997,f1001,f1005,f1009,f1013,f1017,f1021,f1025,f1029,f1034,f1038,f1042,f1046,f1050,f1054,f1059,f1063,f1067,f1071,f1075,f1079,f1084,f1088,f1092,f1096,f1100,f1104,f1109,f1113,f1117,f1121,f1125,f1129,f1134,f1138,f1142,f1195,f1231,f1236,f1240,f1247,f1252,f1256,f1260,f1264,f1268,f1272,f1276,f1280,f1284,f1349,f1558,f1562,f1566,f1571,f1637,f1642,f1673,f1678,f1706,f1711,f1715,f1788,f1794,f1799,f1804,f1808,f1812,f1816,f1821,f1825,f1871,f1877,f1883,f1888,f1892,f1984,f1990,f1996,f2031,f2038,f2043,f2046]) ).
fof(f2046,plain,
( ~ spl40_37
| spl40_185 ),
inference(avatar_contradiction_clause,[],[f2045]) ).
fof(f2045,plain,
( $false
| ~ spl40_37
| spl40_185 ),
inference(trivial_inequality_removal,[],[f2044]) ).
fof(f2044,plain,
( tptp_float_0_0 != tptp_float_0_0
| ~ spl40_37
| spl40_185 ),
inference(superposition,[],[f2037,f638]) ).
fof(f638,plain,
( ! [X0] : tptp_float_0_0 = sum(tptp_float_0_0,tptp_minus_1,X0)
| ~ spl40_37 ),
inference(avatar_component_clause,[],[f637]) ).
fof(f637,plain,
( spl40_37
<=> ! [X0] : tptp_float_0_0 = sum(tptp_float_0_0,tptp_minus_1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_37])]) ).
fof(f2037,plain,
( tptp_float_0_0 != sum(tptp_float_0_0,tptp_minus_1,divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| spl40_185 ),
inference(avatar_component_clause,[],[f2035]) ).
fof(f2035,plain,
( spl40_185
<=> tptp_float_0_0 = sum(tptp_float_0_0,tptp_minus_1,divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_185])]) ).
fof(f2043,plain,
( spl40_186
| ~ spl40_22
| ~ spl40_33
| ~ spl40_35 ),
inference(avatar_split_clause,[],[f662,f628,f611,f553,f2040]) ).
fof(f2040,plain,
( spl40_186
<=> leq(tptp_minus_1,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_186])]) ).
fof(f553,plain,
( spl40_22
<=> gt(n0,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_22])]) ).
fof(f611,plain,
( spl40_33
<=> n0 = tptp_float_0_0 ),
introduced(avatar_definition,[new_symbols(naming,[spl40_33])]) ).
fof(f628,plain,
( spl40_35
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_35])]) ).
fof(f662,plain,
( leq(tptp_minus_1,tptp_float_0_0)
| ~ spl40_22
| ~ spl40_33
| ~ spl40_35 ),
inference(forward_demodulation,[],[f640,f613]) ).
fof(f613,plain,
( n0 = tptp_float_0_0
| ~ spl40_33 ),
inference(avatar_component_clause,[],[f611]) ).
fof(f640,plain,
( leq(tptp_minus_1,n0)
| ~ spl40_22
| ~ spl40_35 ),
inference(resolution,[],[f629,f555]) ).
fof(f555,plain,
( gt(n0,tptp_minus_1)
| ~ spl40_22 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f629,plain,
( ! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,X1) )
| ~ spl40_35 ),
inference(avatar_component_clause,[],[f628]) ).
fof(f2038,plain,
( ~ spl40_185
| ~ spl40_26
| ~ spl40_33
| ~ spl40_42
| spl40_184 ),
inference(avatar_split_clause,[],[f2033,f2028,f691,f611,f571,f2035]) ).
fof(f571,plain,
( spl40_26
<=> n0 = plus(tptp_minus_1,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_26])]) ).
fof(f691,plain,
( spl40_42
<=> ! [X0] : minus(plus(X0,n1),n1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl40_42])]) ).
fof(f2028,plain,
( spl40_184
<=> n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_184])]) ).
fof(f2033,plain,
( tptp_float_0_0 != sum(tptp_float_0_0,tptp_minus_1,divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| ~ spl40_26
| ~ spl40_33
| ~ spl40_42
| spl40_184 ),
inference(forward_demodulation,[],[f2032,f714]) ).
fof(f714,plain,
( tptp_minus_1 = minus(tptp_float_0_0,n1)
| ~ spl40_26
| ~ spl40_33
| ~ spl40_42 ),
inference(forward_demodulation,[],[f708,f613]) ).
fof(f708,plain,
( tptp_minus_1 = minus(n0,n1)
| ~ spl40_26
| ~ spl40_42 ),
inference(superposition,[],[f692,f573]) ).
fof(f573,plain,
( n0 = plus(tptp_minus_1,n1)
| ~ spl40_26 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f692,plain,
( ! [X0] : minus(plus(X0,n1),n1) = X0
| ~ spl40_42 ),
inference(avatar_component_clause,[],[f691]) ).
fof(f2032,plain,
( tptp_float_0_0 != sum(tptp_float_0_0,minus(tptp_float_0_0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| ~ spl40_33
| spl40_184 ),
inference(forward_demodulation,[],[f2030,f613]) ).
fof(f2030,plain,
( n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| spl40_184 ),
inference(avatar_component_clause,[],[f2028]) ).
fof(f2031,plain,
( ~ spl40_184
| ~ spl40_38
| ~ spl40_39 ),
inference(avatar_split_clause,[],[f248,f675,f669,f2028]) ).
fof(f669,plain,
( spl40_38
<=> pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_38])]) ).
fof(f675,plain,
( spl40_39
<=> pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_39])]) ).
fof(f248,plain,
( pv88 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
| pv86 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
( ( pv88 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
| pv86 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) )
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) ),
inference(flattening,[],[f108]) ).
fof(f108,plain,
( ( pv88 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
| pv86 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) )
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,negated_conjecture,
~ ( ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) )
=> ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) ) ),
inference(negated_conjecture,[],[f53]) ).
fof(f53,conjecture,
( ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) )
=> ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0022) ).
fof(f1996,plain,
( spl40_183
| ~ spl40_33
| ~ spl40_182 ),
inference(avatar_split_clause,[],[f1992,f1988,f611,f1994]) ).
fof(f1994,plain,
( spl40_183
<=> ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_183])]) ).
fof(f1988,plain,
( spl40_182
<=> ! [X0] :
( n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_182])]) ).
fof(f1992,plain,
( ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n3) )
| ~ spl40_33
| ~ spl40_182 ),
inference(forward_demodulation,[],[f1991,f613]) ).
fof(f1991,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) )
| ~ spl40_33
| ~ spl40_182 ),
inference(forward_demodulation,[],[f1989,f613]) ).
fof(f1989,plain,
( ! [X0] :
( n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) )
| ~ spl40_182 ),
inference(avatar_component_clause,[],[f1988]) ).
fof(f1990,plain,
spl40_182,
inference(avatar_split_clause,[],[f296,f1988]) ).
fof(f296,plain,
! [X0] :
( n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] :
( n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) ),
inference(flattening,[],[f112]) ).
fof(f112,plain,
! [X0] :
( n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0] :
( ( leq(X0,n3)
& leq(n0,X0) )
=> ( n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_3) ).
fof(f1984,plain,
spl40_181,
inference(avatar_split_clause,[],[f428,f1982]) ).
fof(f1982,plain,
( spl40_181
<=> ! [X3,X4,X0,X6,X2] :
( a_select3(X4,X2,X3) = a_select3(tptp_update3(X4,X0,X3,X6),X2,X3)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_181])]) ).
fof(f428,plain,
! [X2,X3,X0,X6,X4] :
( a_select3(X4,X2,X3) = a_select3(tptp_update3(X4,X0,X3,X6),X2,X3)
| X0 = X2 ),
inference(equality_resolution,[],[f427]) ).
fof(f427,plain,
! [X2,X3,X0,X1,X6,X4] :
( a_select3(X4,X2,X3) = a_select3(tptp_update3(X4,X0,X1,X6),X2,X3)
| X1 != X3
| X0 = X2 ),
inference(equality_resolution,[],[f382]) ).
fof(f382,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( a_select3(tptp_update3(X4,X0,X1,X6),X2,X3) = X5
| a_select3(X4,X2,X3) != X5
| X1 != X3
| X0 = X2 ),
inference(cnf_transformation,[],[f157]) ).
fof(f157,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( a_select3(tptp_update3(X4,X0,X1,X6),X2,X3) = X5
| a_select3(X4,X2,X3) != X5
| X1 != X3
| X0 = X2 ),
inference(flattening,[],[f156]) ).
fof(f156,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( a_select3(tptp_update3(X4,X0,X1,X6),X2,X3) = X5
| a_select3(X4,X2,X3) != X5
| X1 != X3
| X0 = X2 ),
inference(ennf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( a_select3(X4,X2,X3) = X5
& X1 = X3
& X0 != X2 )
=> a_select3(tptp_update3(X4,X0,X1,X6),X2,X3) = X5 ),
inference(rectify,[],[f46]) ).
fof(f46,axiom,
! [X4,X10,X6,X23,X0,X16,X24] :
( ( a_select3(X0,X6,X23) = X16
& X10 = X23
& X4 != X6 )
=> a_select3(tptp_update3(X0,X4,X10,X24),X6,X23) = X16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel3_update_2) ).
fof(f1892,plain,
( spl40_180
| ~ spl40_33
| ~ spl40_177 ),
inference(avatar_split_clause,[],[f1879,f1875,f611,f1890]) ).
fof(f1890,plain,
( spl40_180
<=> ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_180])]) ).
fof(f1875,plain,
( spl40_177
<=> ! [X0] :
( n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_177])]) ).
fof(f1879,plain,
( ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n2) )
| ~ spl40_33
| ~ spl40_177 ),
inference(forward_demodulation,[],[f1878,f613]) ).
fof(f1878,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) )
| ~ spl40_33
| ~ spl40_177 ),
inference(forward_demodulation,[],[f1876,f613]) ).
fof(f1876,plain,
( ! [X0] :
( n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) )
| ~ spl40_177 ),
inference(avatar_component_clause,[],[f1875]) ).
fof(f1888,plain,
( spl40_179
| ~ spl40_15
| ~ spl40_35 ),
inference(avatar_split_clause,[],[f661,f628,f518,f1885]) ).
fof(f1885,plain,
( spl40_179
<=> leq(n4,n5) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_179])]) ).
fof(f518,plain,
( spl40_15
<=> gt(n5,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_15])]) ).
fof(f661,plain,
( leq(n4,n5)
| ~ spl40_15
| ~ spl40_35 ),
inference(resolution,[],[f629,f520]) ).
fof(f520,plain,
( gt(n5,n4)
| ~ spl40_15 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f1883,plain,
spl40_178,
inference(avatar_split_clause,[],[f365,f1881]) ).
fof(f1881,plain,
( spl40_178
<=> ! [X0,X3,X2,X1] :
( a_select2(tptp_const_array1(dim(X1,X2),X3),X0) = X3
| ~ leq(X0,X2)
| ~ leq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_178])]) ).
fof(f365,plain,
! [X2,X3,X0,X1] :
( a_select2(tptp_const_array1(dim(X1,X2),X3),X0) = X3
| ~ leq(X0,X2)
| ~ leq(X1,X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0,X1,X2,X3] :
( a_select2(tptp_const_array1(dim(X1,X2),X3),X0) = X3
| ~ leq(X0,X2)
| ~ leq(X1,X0) ),
inference(flattening,[],[f146]) ).
fof(f146,plain,
! [X0,X1,X2,X3] :
( a_select2(tptp_const_array1(dim(X1,X2),X3),X0) = X3
| ~ leq(X0,X2)
| ~ leq(X1,X0) ),
inference(ennf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1,X2,X3] :
( ( leq(X0,X2)
& leq(X1,X0) )
=> a_select2(tptp_const_array1(dim(X1,X2),X3),X0) = X3 ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X4,X5,X6,X7] :
( ( leq(X4,X6)
& leq(X5,X4) )
=> a_select2(tptp_const_array1(dim(X5,X6),X7),X4) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',const_array1_select) ).
fof(f1877,plain,
spl40_177,
inference(avatar_split_clause,[],[f297,f1875]) ).
fof(f297,plain,
! [X0] :
( n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0] :
( n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) ),
inference(flattening,[],[f114]) ).
fof(f114,plain,
! [X0] :
( n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,axiom,
! [X0] :
( ( leq(X0,n2)
& leq(n0,X0) )
=> ( n2 = X0
| n1 = X0
| n0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_2) ).
fof(f1871,plain,
spl40_176,
inference(avatar_split_clause,[],[f426,f1869]) ).
fof(f1869,plain,
( spl40_176
<=> ! [X2,X4,X0,X1] :
( a_select2(X2,X1) = a_select2(tptp_update2(X2,X0,X4),X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_176])]) ).
fof(f426,plain,
! [X2,X0,X1,X4] :
( a_select2(X2,X1) = a_select2(tptp_update2(X2,X0,X4),X1)
| X0 = X1 ),
inference(equality_resolution,[],[f375]) ).
fof(f375,plain,
! [X2,X3,X0,X1,X4] :
( a_select2(tptp_update2(X2,X0,X4),X1) = X3
| a_select2(X2,X1) != X3
| X0 = X1 ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0,X1,X2,X3,X4] :
( a_select2(tptp_update2(X2,X0,X4),X1) = X3
| a_select2(X2,X1) != X3
| X0 = X1 ),
inference(flattening,[],[f152]) ).
fof(f152,plain,
! [X0,X1,X2,X3,X4] :
( a_select2(tptp_update2(X2,X0,X4),X1) = X3
| a_select2(X2,X1) != X3
| X0 = X1 ),
inference(ennf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2,X3,X4] :
( ( a_select2(X2,X1) = X3
& X0 != X1 )
=> a_select2(tptp_update2(X2,X0,X4),X1) = X3 ),
inference(rectify,[],[f49]) ).
fof(f49,axiom,
! [X4,X6,X0,X16,X24] :
( ( a_select2(X0,X6) = X16
& X4 != X6 )
=> a_select2(tptp_update2(X0,X4,X24),X6) = X16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel2_update_2) ).
fof(f1825,plain,
( spl40_175
| ~ spl40_33
| ~ spl40_169 ),
inference(avatar_split_clause,[],[f1800,f1797,f611,f1823]) ).
fof(f1823,plain,
( spl40_175
<=> ! [X0,X3,X2,X1] :
( leq(tptp_float_0_0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_175])]) ).
fof(f1797,plain,
( spl40_169
<=> ! [X0,X3,X2,X1] :
( leq(n0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_169])]) ).
fof(f1800,plain,
( ! [X2,X3,X0,X1] :
( leq(tptp_float_0_0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) )
| ~ spl40_33
| ~ spl40_169 ),
inference(forward_demodulation,[],[f1798,f613]) ).
fof(f1798,plain,
( ! [X2,X3,X0,X1] :
( leq(n0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) )
| ~ spl40_169 ),
inference(avatar_component_clause,[],[f1797]) ).
fof(f1821,plain,
( spl40_174
| ~ spl40_16
| ~ spl40_35 ),
inference(avatar_split_clause,[],[f660,f628,f523,f1818]) ).
fof(f1818,plain,
( spl40_174
<=> leq(n3,n5) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_174])]) ).
fof(f523,plain,
( spl40_16
<=> gt(n5,n3) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_16])]) ).
fof(f660,plain,
( leq(n3,n5)
| ~ spl40_16
| ~ spl40_35 ),
inference(resolution,[],[f629,f525]) ).
fof(f525,plain,
( gt(n5,n3)
| ~ spl40_16 ),
inference(avatar_component_clause,[],[f523]) ).
fof(f1816,plain,
( spl40_173
| ~ spl40_33
| ~ spl40_168 ),
inference(avatar_split_clause,[],[f1795,f1792,f611,f1814]) ).
fof(f1814,plain,
( spl40_173
<=> ! [X0,X3,X2,X1] :
( leq(tptp_float_0_0,sK32(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_173])]) ).
fof(f1792,plain,
( spl40_168
<=> ! [X0,X3,X2,X1] :
( leq(n0,sK32(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_168])]) ).
fof(f1795,plain,
( ! [X2,X3,X0,X1] :
( leq(tptp_float_0_0,sK32(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) )
| ~ spl40_33
| ~ spl40_168 ),
inference(forward_demodulation,[],[f1793,f613]) ).
fof(f1793,plain,
( ! [X2,X3,X0,X1] :
( leq(n0,sK32(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) )
| ~ spl40_168 ),
inference(avatar_component_clause,[],[f1792]) ).
fof(f1812,plain,
( spl40_172
| ~ spl40_33
| ~ spl40_167 ),
inference(avatar_split_clause,[],[f1790,f1786,f611,f1810]) ).
fof(f1810,plain,
( spl40_172
<=> ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n1 = X0
| ~ leq(X0,n1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_172])]) ).
fof(f1786,plain,
( spl40_167
<=> ! [X0] :
( n1 = X0
| n0 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_167])]) ).
fof(f1790,plain,
( ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n1 = X0
| ~ leq(X0,n1) )
| ~ spl40_33
| ~ spl40_167 ),
inference(forward_demodulation,[],[f1789,f613]) ).
fof(f1789,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| n1 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) )
| ~ spl40_33
| ~ spl40_167 ),
inference(forward_demodulation,[],[f1787,f613]) ).
fof(f1787,plain,
( ! [X0] :
( n1 = X0
| n0 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) )
| ~ spl40_167 ),
inference(avatar_component_clause,[],[f1786]) ).
fof(f1808,plain,
spl40_171,
inference(avatar_split_clause,[],[f379,f1806]) ).
fof(f1806,plain,
( spl40_171
<=> ! [X0,X3,X2,X1] :
( leq(sK33(X0,X1,X2,X3),X2)
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_171])]) ).
fof(f379,plain,
! [X2,X3,X0,X1] :
( leq(sK33(X0,X1,X2,X3),X2)
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f232]) ).
fof(f232,plain,
! [X0,X1,X2,X3] :
( ( a_select3(X1,sK32(X0,X1,X2,X3),sK33(X0,X1,X2,X3)) != X0
& leq(sK33(X0,X1,X2,X3),X2)
& leq(sK32(X0,X1,X2,X3),X3)
& leq(n0,sK33(X0,X1,X2,X3))
& leq(n0,sK32(X0,X1,X2,X3)) )
| ~ sP9(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33])],[f230,f231]) ).
fof(f231,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5] :
( a_select3(X1,X4,X5) != X0
& leq(X5,X2)
& leq(X4,X3)
& leq(n0,X5)
& leq(n0,X4) )
=> ( a_select3(X1,sK32(X0,X1,X2,X3),sK33(X0,X1,X2,X3)) != X0
& leq(sK33(X0,X1,X2,X3),X2)
& leq(sK32(X0,X1,X2,X3),X3)
& leq(n0,sK33(X0,X1,X2,X3))
& leq(n0,sK32(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f230,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5] :
( a_select3(X1,X4,X5) != X0
& leq(X5,X2)
& leq(X4,X3)
& leq(n0,X5)
& leq(n0,X4) )
| ~ sP9(X0,X1,X2,X3) ),
inference(rectify,[],[f229]) ).
fof(f229,plain,
! [X5,X4,X3,X2] :
( ? [X6,X7] :
( a_select3(X4,X6,X7) != X5
& leq(X7,X3)
& leq(X6,X2)
& leq(n0,X7)
& leq(n0,X6) )
| ~ sP9(X5,X4,X3,X2) ),
inference(nnf_transformation,[],[f178]) ).
fof(f178,plain,
! [X5,X4,X3,X2] :
( ? [X6,X7] :
( a_select3(X4,X6,X7) != X5
& leq(X7,X3)
& leq(X6,X2)
& leq(n0,X7)
& leq(n0,X6) )
| ~ sP9(X5,X4,X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f1804,plain,
spl40_170,
inference(avatar_split_clause,[],[f378,f1802]) ).
fof(f1802,plain,
( spl40_170
<=> ! [X0,X3,X2,X1] :
( leq(sK32(X0,X1,X2,X3),X3)
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_170])]) ).
fof(f378,plain,
! [X2,X3,X0,X1] :
( leq(sK32(X0,X1,X2,X3),X3)
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f232]) ).
fof(f1799,plain,
spl40_169,
inference(avatar_split_clause,[],[f377,f1797]) ).
fof(f377,plain,
! [X2,X3,X0,X1] :
( leq(n0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f232]) ).
fof(f1794,plain,
spl40_168,
inference(avatar_split_clause,[],[f376,f1792]) ).
fof(f376,plain,
! [X2,X3,X0,X1] :
( leq(n0,sK32(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f232]) ).
fof(f1788,plain,
spl40_167,
inference(avatar_split_clause,[],[f299,f1786]) ).
fof(f299,plain,
! [X0] :
( n1 = X0
| n0 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0] :
( n1 = X0
| n0 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) ),
inference(flattening,[],[f118]) ).
fof(f118,plain,
! [X0] :
( n1 = X0
| n0 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0] :
( ( leq(X0,n1)
& leq(n0,X0) )
=> ( n1 = X0
| n0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_1) ).
fof(f1715,plain,
spl40_166,
inference(avatar_split_clause,[],[f446,f1713]) ).
fof(f1713,plain,
( spl40_166
<=> ! [X0] : plus(n5,X0) = plus(plus(n2,plus(n2,X0)),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_166])]) ).
fof(f446,plain,
! [X0] : plus(n5,X0) = plus(plus(n2,plus(n2,X0)),n1),
inference(forward_demodulation,[],[f445,f410]) ).
fof(f410,plain,
! [X0] : plus(n2,X0) = plus(plus(X0,n1),n1),
inference(definition_unfolding,[],[f287,f283,f283]) ).
fof(f283,plain,
! [X0] : succ(X0) = plus(X0,n1),
inference(cnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] : succ(X0) = plus(X0,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_1_r) ).
fof(f287,plain,
! [X0] : succ(succ(X0)) = plus(n2,X0),
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] : succ(succ(X0)) = plus(n2,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_2_l) ).
fof(f445,plain,
! [X0] : plus(n5,X0) = plus(plus(n2,plus(plus(X0,n1),n1)),n1),
inference(forward_demodulation,[],[f417,f410]) ).
fof(f417,plain,
! [X0] : plus(n5,X0) = plus(plus(plus(plus(plus(X0,n1),n1),n1),n1),n1),
inference(definition_unfolding,[],[f294,f283,f283,f283,f283,f283]) ).
fof(f294,plain,
! [X0] : succ(succ(succ(succ(succ(X0))))) = plus(n5,X0),
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] : succ(succ(succ(succ(succ(X0))))) = plus(n5,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_5_l) ).
fof(f1711,plain,
( spl40_165
| ~ spl40_17
| ~ spl40_35 ),
inference(avatar_split_clause,[],[f659,f628,f528,f1708]) ).
fof(f1708,plain,
( spl40_165
<=> leq(n2,n5) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_165])]) ).
fof(f528,plain,
( spl40_17
<=> gt(n5,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_17])]) ).
fof(f659,plain,
( leq(n2,n5)
| ~ spl40_17
| ~ spl40_35 ),
inference(resolution,[],[f629,f530]) ).
fof(f530,plain,
( gt(n5,n2)
| ~ spl40_17 ),
inference(avatar_component_clause,[],[f528]) ).
fof(f1706,plain,
spl40_164,
inference(avatar_split_clause,[],[f444,f1704]) ).
fof(f1704,plain,
( spl40_164
<=> ! [X0] : plus(X0,n5) = plus(plus(n2,plus(n2,X0)),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_164])]) ).
fof(f444,plain,
! [X0] : plus(X0,n5) = plus(plus(n2,plus(n2,X0)),n1),
inference(forward_demodulation,[],[f443,f410]) ).
fof(f443,plain,
! [X0] : plus(X0,n5) = plus(plus(n2,plus(plus(X0,n1),n1)),n1),
inference(forward_demodulation,[],[f416,f410]) ).
fof(f416,plain,
! [X0] : plus(X0,n5) = plus(plus(plus(plus(plus(X0,n1),n1),n1),n1),n1),
inference(definition_unfolding,[],[f293,f283,f283,f283,f283,f283]) ).
fof(f293,plain,
! [X0] : plus(X0,n5) = succ(succ(succ(succ(succ(X0))))),
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] : plus(X0,n5) = succ(succ(succ(succ(succ(X0))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_5_r) ).
fof(f1678,plain,
( spl40_163
| ~ spl40_150
| ~ spl40_152
| ~ spl40_162 ),
inference(avatar_split_clause,[],[f1674,f1671,f1274,f1266,f1676]) ).
fof(f1676,plain,
( spl40_163
<=> ! [X0] : plus(n4,X0) = plus(plus(X0,n3),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_163])]) ).
fof(f1266,plain,
( spl40_150
<=> ! [X0] : plus(n2,X0) = plus(plus(X0,n1),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_150])]) ).
fof(f1274,plain,
( spl40_152
<=> ! [X0] : plus(X0,n3) = plus(plus(n2,X0),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_152])]) ).
fof(f1671,plain,
( spl40_162
<=> ! [X0] : plus(n4,X0) = plus(plus(n2,plus(X0,n1)),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_162])]) ).
fof(f1674,plain,
( ! [X0] : plus(n4,X0) = plus(plus(X0,n3),n1)
| ~ spl40_150
| ~ spl40_152
| ~ spl40_162 ),
inference(forward_demodulation,[],[f1672,f1454]) ).
fof(f1454,plain,
( ! [X0] : plus(X0,n3) = plus(n2,plus(X0,n1))
| ~ spl40_150
| ~ spl40_152 ),
inference(forward_demodulation,[],[f1438,f1275]) ).
fof(f1275,plain,
( ! [X0] : plus(X0,n3) = plus(plus(n2,X0),n1)
| ~ spl40_152 ),
inference(avatar_component_clause,[],[f1274]) ).
fof(f1438,plain,
( ! [X0] : plus(n2,plus(X0,n1)) = plus(plus(n2,X0),n1)
| ~ spl40_150 ),
inference(superposition,[],[f1267,f1267]) ).
fof(f1267,plain,
( ! [X0] : plus(n2,X0) = plus(plus(X0,n1),n1)
| ~ spl40_150 ),
inference(avatar_component_clause,[],[f1266]) ).
fof(f1672,plain,
( ! [X0] : plus(n4,X0) = plus(plus(n2,plus(X0,n1)),n1)
| ~ spl40_162 ),
inference(avatar_component_clause,[],[f1671]) ).
fof(f1673,plain,
spl40_162,
inference(avatar_split_clause,[],[f442,f1671]) ).
fof(f442,plain,
! [X0] : plus(n4,X0) = plus(plus(n2,plus(X0,n1)),n1),
inference(forward_demodulation,[],[f415,f410]) ).
fof(f415,plain,
! [X0] : plus(n4,X0) = plus(plus(plus(plus(X0,n1),n1),n1),n1),
inference(definition_unfolding,[],[f292,f283,f283,f283,f283]) ).
fof(f292,plain,
! [X0] : succ(succ(succ(succ(X0)))) = plus(n4,X0),
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] : succ(succ(succ(succ(X0)))) = plus(n4,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_4_l) ).
fof(f1642,plain,
( spl40_161
| ~ spl40_150
| ~ spl40_152
| ~ spl40_160 ),
inference(avatar_split_clause,[],[f1638,f1635,f1274,f1266,f1640]) ).
fof(f1640,plain,
( spl40_161
<=> ! [X0] : plus(X0,n4) = plus(plus(X0,n3),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_161])]) ).
fof(f1635,plain,
( spl40_160
<=> ! [X0] : plus(X0,n4) = plus(plus(n2,plus(X0,n1)),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_160])]) ).
fof(f1638,plain,
( ! [X0] : plus(X0,n4) = plus(plus(X0,n3),n1)
| ~ spl40_150
| ~ spl40_152
| ~ spl40_160 ),
inference(forward_demodulation,[],[f1636,f1454]) ).
fof(f1636,plain,
( ! [X0] : plus(X0,n4) = plus(plus(n2,plus(X0,n1)),n1)
| ~ spl40_160 ),
inference(avatar_component_clause,[],[f1635]) ).
fof(f1637,plain,
spl40_160,
inference(avatar_split_clause,[],[f441,f1635]) ).
fof(f441,plain,
! [X0] : plus(X0,n4) = plus(plus(n2,plus(X0,n1)),n1),
inference(forward_demodulation,[],[f414,f410]) ).
fof(f414,plain,
! [X0] : plus(X0,n4) = plus(plus(plus(plus(X0,n1),n1),n1),n1),
inference(definition_unfolding,[],[f291,f283,f283,f283,f283]) ).
fof(f291,plain,
! [X0] : plus(X0,n4) = succ(succ(succ(succ(X0)))),
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] : plus(X0,n4) = succ(succ(succ(succ(X0)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_4_r) ).
fof(f1571,plain,
( spl40_159
| ~ spl40_18
| ~ spl40_35 ),
inference(avatar_split_clause,[],[f658,f628,f533,f1568]) ).
fof(f1568,plain,
( spl40_159
<=> leq(n1,n5) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_159])]) ).
fof(f533,plain,
( spl40_18
<=> gt(n5,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_18])]) ).
fof(f658,plain,
( leq(n1,n5)
| ~ spl40_18
| ~ spl40_35 ),
inference(resolution,[],[f629,f535]) ).
fof(f535,plain,
( gt(n5,n1)
| ~ spl40_18 ),
inference(avatar_component_clause,[],[f533]) ).
fof(f1566,plain,
spl40_158,
inference(avatar_split_clause,[],[f425,f1564]) ).
fof(f1564,plain,
( spl40_158
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ leq(plus(X0,n1),plus(X1,n1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_158])]) ).
fof(f425,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ leq(plus(X0,n1),plus(X1,n1)) ),
inference(definition_unfolding,[],[f331,f283,f283]) ).
fof(f331,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ leq(succ(X0),succ(X1)) ),
inference(cnf_transformation,[],[f198]) ).
fof(f198,plain,
! [X0,X1] :
( ( leq(succ(X0),succ(X1))
| ~ leq(X0,X1) )
& ( leq(X0,X1)
| ~ leq(succ(X0),succ(X1)) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] :
( leq(succ(X0),succ(X1))
<=> leq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_succ) ).
fof(f1562,plain,
spl40_157,
inference(avatar_split_clause,[],[f424,f1560]) ).
fof(f1560,plain,
( spl40_157
<=> ! [X0,X1] :
( leq(plus(X0,n1),plus(X1,n1))
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_157])]) ).
fof(f424,plain,
! [X0,X1] :
( leq(plus(X0,n1),plus(X1,n1))
| ~ leq(X0,X1) ),
inference(definition_unfolding,[],[f332,f283,f283]) ).
fof(f332,plain,
! [X0,X1] :
( leq(succ(X0),succ(X1))
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f198]) ).
fof(f1558,plain,
spl40_156,
inference(avatar_split_clause,[],[f364,f1556]) ).
fof(f1556,plain,
( spl40_156
<=> ! [X2,X0,X1,X3] : a_select3(tptp_update3(X0,X1,X2,X3),X1,X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl40_156])]) ).
fof(f364,plain,
! [X2,X3,X0,X1] : a_select3(tptp_update3(X0,X1,X2,X3),X1,X2) = X3,
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2,X3] : a_select3(tptp_update3(X0,X1,X2,X3),X1,X2) = X3,
inference(rectify,[],[f45]) ).
fof(f45,axiom,
! [X0,X6,X23,X16] : a_select3(tptp_update3(X0,X6,X23,X16),X6,X23) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel3_update_1) ).
fof(f1349,plain,
( spl40_155
| ~ spl40_14
| ~ spl40_35 ),
inference(avatar_split_clause,[],[f657,f628,f513,f1346]) ).
fof(f1346,plain,
( spl40_155
<=> leq(tptp_minus_1,n5) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_155])]) ).
fof(f513,plain,
( spl40_14
<=> gt(n5,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_14])]) ).
fof(f657,plain,
( leq(tptp_minus_1,n5)
| ~ spl40_14
| ~ spl40_35 ),
inference(resolution,[],[f629,f515]) ).
fof(f515,plain,
( gt(n5,tptp_minus_1)
| ~ spl40_14 ),
inference(avatar_component_clause,[],[f513]) ).
fof(f1284,plain,
( spl40_154
| ~ spl40_33
| ~ spl40_144 ),
inference(avatar_split_clause,[],[f1243,f1238,f611,f1282]) ).
fof(f1282,plain,
( spl40_154
<=> ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| ~ leq(X0,tptp_float_0_0)
| tptp_float_0_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_154])]) ).
fof(f1238,plain,
( spl40_144
<=> ! [X0] :
( n0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_144])]) ).
fof(f1243,plain,
( ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| ~ leq(X0,tptp_float_0_0)
| tptp_float_0_0 = X0 )
| ~ spl40_33
| ~ spl40_144 ),
inference(forward_demodulation,[],[f1242,f613]) ).
fof(f1242,plain,
( ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| tptp_float_0_0 = X0
| ~ leq(n0,X0) )
| ~ spl40_33
| ~ spl40_144 ),
inference(forward_demodulation,[],[f1241,f613]) ).
fof(f1241,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) )
| ~ spl40_33
| ~ spl40_144 ),
inference(forward_demodulation,[],[f1239,f613]) ).
fof(f1239,plain,
( ! [X0] :
( n0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) )
| ~ spl40_144 ),
inference(avatar_component_clause,[],[f1238]) ).
fof(f1280,plain,
spl40_153,
inference(avatar_split_clause,[],[f440,f1278]) ).
fof(f1278,plain,
( spl40_153
<=> ! [X0] : plus(n3,X0) = plus(plus(n2,X0),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_153])]) ).
fof(f440,plain,
! [X0] : plus(n3,X0) = plus(plus(n2,X0),n1),
inference(forward_demodulation,[],[f413,f410]) ).
fof(f413,plain,
! [X0] : plus(n3,X0) = plus(plus(plus(X0,n1),n1),n1),
inference(definition_unfolding,[],[f290,f283,f283,f283]) ).
fof(f290,plain,
! [X0] : succ(succ(succ(X0))) = plus(n3,X0),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] : succ(succ(succ(X0))) = plus(n3,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_3_l) ).
fof(f1276,plain,
spl40_152,
inference(avatar_split_clause,[],[f439,f1274]) ).
fof(f439,plain,
! [X0] : plus(X0,n3) = plus(plus(n2,X0),n1),
inference(forward_demodulation,[],[f412,f410]) ).
fof(f412,plain,
! [X0] : plus(X0,n3) = plus(plus(plus(X0,n1),n1),n1),
inference(definition_unfolding,[],[f289,f283,f283,f283]) ).
fof(f289,plain,
! [X0] : plus(X0,n3) = succ(succ(succ(X0))),
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] : plus(X0,n3) = succ(succ(succ(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_3_r) ).
fof(f1272,plain,
spl40_151,
inference(avatar_split_clause,[],[f411,f1270]) ).
fof(f1270,plain,
( spl40_151
<=> ! [X0] : plus(X0,n2) = plus(plus(X0,n1),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_151])]) ).
fof(f411,plain,
! [X0] : plus(X0,n2) = plus(plus(X0,n1),n1),
inference(definition_unfolding,[],[f288,f283,f283]) ).
fof(f288,plain,
! [X0] : plus(X0,n2) = succ(succ(X0)),
inference(cnf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] : plus(X0,n2) = succ(succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_2_r) ).
fof(f1268,plain,
spl40_150,
inference(avatar_split_clause,[],[f410,f1266]) ).
fof(f1264,plain,
spl40_149,
inference(avatar_split_clause,[],[f335,f1262]) ).
fof(f1262,plain,
( spl40_149
<=> ! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_149])]) ).
fof(f335,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(flattening,[],[f138]) ).
fof(f138,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( leq(X1,X2)
& leq(X0,X1) )
=> leq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_leq) ).
fof(f1260,plain,
spl40_148,
inference(avatar_split_clause,[],[f334,f1258]) ).
fof(f1258,plain,
( spl40_148
<=> ! [X2,X0,X1] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_148])]) ).
fof(f334,plain,
! [X2,X0,X1] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0,X1,X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1) ),
inference(flattening,[],[f136]) ).
fof(f136,plain,
! [X0,X1,X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( gt(X1,X2)
& gt(X0,X1) )
=> gt(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_gt) ).
fof(f1256,plain,
spl40_147,
inference(avatar_split_clause,[],[f308,f1254]) ).
fof(f1254,plain,
( spl40_147
<=> ! [X0,X1] :
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_147])]) ).
fof(f308,plain,
! [X0,X1] :
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0,X1] :
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0,X1] :
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( X0 != X1
& leq(X0,X1) )
=> gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt2) ).
fof(f1252,plain,
( spl40_146
| ~ spl40_3
| ~ spl40_35 ),
inference(avatar_split_clause,[],[f655,f628,f458,f1249]) ).
fof(f1249,plain,
( spl40_146
<=> leq(n3,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_146])]) ).
fof(f458,plain,
( spl40_3
<=> gt(n4,n3) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_3])]) ).
fof(f655,plain,
( leq(n3,n4)
| ~ spl40_3
| ~ spl40_35 ),
inference(resolution,[],[f629,f460]) ).
fof(f460,plain,
( gt(n4,n3)
| ~ spl40_3 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f1247,plain,
spl40_145,
inference(avatar_split_clause,[],[f301,f1245]) ).
fof(f1245,plain,
( spl40_145
<=> ! [X0,X1] :
( X0 = X1
| gt(X1,X0)
| gt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_145])]) ).
fof(f301,plain,
! [X0,X1] :
( X0 = X1
| gt(X1,X0)
| gt(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( X0 = X1
| gt(X1,X0)
| gt(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).
fof(f1240,plain,
spl40_144,
inference(avatar_split_clause,[],[f300,f1238]) ).
fof(f300,plain,
! [X0] :
( n0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0] :
( n0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0] :
( n0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0] :
( ( leq(X0,n0)
& leq(n0,X0) )
=> n0 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_0) ).
fof(f1236,plain,
( spl40_143
| ~ spl40_4
| ~ spl40_35 ),
inference(avatar_split_clause,[],[f654,f628,f463,f1233]) ).
fof(f1233,plain,
( spl40_143
<=> leq(n2,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_143])]) ).
fof(f463,plain,
( spl40_4
<=> gt(n4,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_4])]) ).
fof(f654,plain,
( leq(n2,n4)
| ~ spl40_4
| ~ spl40_35 ),
inference(resolution,[],[f629,f465]) ).
fof(f465,plain,
( gt(n4,n2)
| ~ spl40_4 ),
inference(avatar_component_clause,[],[f463]) ).
fof(f1231,plain,
( spl40_142
| ~ spl40_5
| ~ spl40_35 ),
inference(avatar_split_clause,[],[f653,f628,f468,f1228]) ).
fof(f1228,plain,
( spl40_142
<=> leq(n1,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_142])]) ).
fof(f468,plain,
( spl40_5
<=> gt(n4,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_5])]) ).
fof(f653,plain,
( leq(n1,n4)
| ~ spl40_5
| ~ spl40_35 ),
inference(resolution,[],[f629,f470]) ).
fof(f470,plain,
( gt(n4,n1)
| ~ spl40_5 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f1195,plain,
( spl40_141
| ~ spl40_2
| ~ spl40_35 ),
inference(avatar_split_clause,[],[f652,f628,f453,f1192]) ).
fof(f1192,plain,
( spl40_141
<=> leq(tptp_minus_1,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_141])]) ).
fof(f453,plain,
( spl40_2
<=> gt(n4,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_2])]) ).
fof(f652,plain,
( leq(tptp_minus_1,n4)
| ~ spl40_2
| ~ spl40_35 ),
inference(resolution,[],[f629,f455]) ).
fof(f455,plain,
( gt(n4,tptp_minus_1)
| ~ spl40_2 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f1142,plain,
( spl40_140
| ~ spl40_33
| ~ spl40_100 ),
inference(avatar_split_clause,[],[f976,f973,f611,f1140]) ).
fof(f1140,plain,
( spl40_140
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK39(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_140])]) ).
fof(f973,plain,
( spl40_100
<=> ! [X0,X1] :
( leq(n0,sK39(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_100])]) ).
fof(f976,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK39(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl40_33
| ~ spl40_100 ),
inference(forward_demodulation,[],[f974,f613]) ).
fof(f974,plain,
( ! [X0,X1] :
( leq(n0,sK39(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl40_100 ),
inference(avatar_component_clause,[],[f973]) ).
fof(f1138,plain,
( spl40_139
| ~ spl40_33
| ~ spl40_98 ),
inference(avatar_split_clause,[],[f967,f964,f611,f1136]) ).
fof(f1136,plain,
( spl40_139
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK38(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_139])]) ).
fof(f964,plain,
( spl40_98
<=> ! [X0,X1] :
( leq(n0,sK38(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_98])]) ).
fof(f967,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK38(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl40_33
| ~ spl40_98 ),
inference(forward_demodulation,[],[f965,f613]) ).
fof(f965,plain,
( ! [X0,X1] :
( leq(n0,sK38(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl40_98 ),
inference(avatar_component_clause,[],[f964]) ).
fof(f1134,plain,
( spl40_138
| ~ spl40_8
| ~ spl40_35 ),
inference(avatar_split_clause,[],[f650,f628,f483,f1131]) ).
fof(f1131,plain,
( spl40_138
<=> leq(n2,n3) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_138])]) ).
fof(f483,plain,
( spl40_8
<=> gt(n3,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_8])]) ).
fof(f650,plain,
( leq(n2,n3)
| ~ spl40_8
| ~ spl40_35 ),
inference(resolution,[],[f629,f485]) ).
fof(f485,plain,
( gt(n3,n2)
| ~ spl40_8 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f1129,plain,
( spl40_137
| ~ spl40_33
| ~ spl40_96 ),
inference(avatar_split_clause,[],[f958,f955,f611,f1127]) ).
fof(f1127,plain,
( spl40_137
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK37(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_137])]) ).
fof(f955,plain,
( spl40_96
<=> ! [X0,X1] :
( leq(n0,sK37(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_96])]) ).
fof(f958,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK37(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl40_33
| ~ spl40_96 ),
inference(forward_demodulation,[],[f956,f613]) ).
fof(f956,plain,
( ! [X0,X1] :
( leq(n0,sK37(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl40_96 ),
inference(avatar_component_clause,[],[f955]) ).
fof(f1125,plain,
( spl40_136
| ~ spl40_33
| ~ spl40_94 ),
inference(avatar_split_clause,[],[f948,f945,f611,f1123]) ).
fof(f1123,plain,
( spl40_136
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK36(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_136])]) ).
fof(f945,plain,
( spl40_94
<=> ! [X0,X1] :
( leq(n0,sK36(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_94])]) ).
fof(f948,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK36(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl40_33
| ~ spl40_94 ),
inference(forward_demodulation,[],[f946,f613]) ).
fof(f946,plain,
( ! [X0,X1] :
( leq(n0,sK36(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl40_94 ),
inference(avatar_component_clause,[],[f945]) ).
fof(f1121,plain,
( spl40_135
| ~ spl40_33
| ~ spl40_92 ),
inference(avatar_split_clause,[],[f939,f936,f611,f1119]) ).
fof(f1119,plain,
( spl40_135
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK35(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_135])]) ).
fof(f936,plain,
( spl40_92
<=> ! [X0,X1] :
( leq(n0,sK35(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_92])]) ).
fof(f939,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK35(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl40_33
| ~ spl40_92 ),
inference(forward_demodulation,[],[f937,f613]) ).
fof(f937,plain,
( ! [X0,X1] :
( leq(n0,sK35(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl40_92 ),
inference(avatar_component_clause,[],[f936]) ).
fof(f1117,plain,
( spl40_134
| ~ spl40_33
| ~ spl40_90 ),
inference(avatar_split_clause,[],[f930,f927,f611,f1115]) ).
fof(f1115,plain,
( spl40_134
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK34(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_134])]) ).
fof(f927,plain,
( spl40_90
<=> ! [X0,X1] :
( leq(n0,sK34(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_90])]) ).
fof(f930,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK34(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl40_33
| ~ spl40_90 ),
inference(forward_demodulation,[],[f928,f613]) ).
fof(f928,plain,
( ! [X0,X1] :
( leq(n0,sK34(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl40_90 ),
inference(avatar_component_clause,[],[f927]) ).
fof(f1113,plain,
( spl40_133
| ~ spl40_33
| ~ spl40_88 ),
inference(avatar_split_clause,[],[f921,f918,f611,f1111]) ).
fof(f1111,plain,
( spl40_133
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK31(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_133])]) ).
fof(f918,plain,
( spl40_88
<=> ! [X0,X1] :
( leq(n0,sK31(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_88])]) ).
fof(f921,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK31(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl40_33
| ~ spl40_88 ),
inference(forward_demodulation,[],[f919,f613]) ).
fof(f919,plain,
( ! [X0,X1] :
( leq(n0,sK31(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl40_88 ),
inference(avatar_component_clause,[],[f918]) ).
fof(f1109,plain,
( spl40_132
| ~ spl40_9
| ~ spl40_35 ),
inference(avatar_split_clause,[],[f649,f628,f488,f1106]) ).
fof(f1106,plain,
( spl40_132
<=> leq(n1,n3) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_132])]) ).
fof(f488,plain,
( spl40_9
<=> gt(n3,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_9])]) ).
fof(f649,plain,
( leq(n1,n3)
| ~ spl40_9
| ~ spl40_35 ),
inference(resolution,[],[f629,f490]) ).
fof(f490,plain,
( gt(n3,n1)
| ~ spl40_9 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f1104,plain,
( spl40_131
| ~ spl40_33
| ~ spl40_86 ),
inference(avatar_split_clause,[],[f912,f909,f611,f1102]) ).
fof(f1102,plain,
( spl40_131
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK30(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_131])]) ).
fof(f909,plain,
( spl40_86
<=> ! [X0,X1] :
( leq(n0,sK30(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_86])]) ).
fof(f912,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK30(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl40_33
| ~ spl40_86 ),
inference(forward_demodulation,[],[f910,f613]) ).
fof(f910,plain,
( ! [X0,X1] :
( leq(n0,sK30(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl40_86 ),
inference(avatar_component_clause,[],[f909]) ).
fof(f1100,plain,
( spl40_130
| ~ spl40_33
| ~ spl40_83 ),
inference(avatar_split_clause,[],[f898,f895,f611,f1098]) ).
fof(f1098,plain,
( spl40_130
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK28(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_130])]) ).
fof(f895,plain,
( spl40_83
<=> ! [X0,X1] :
( leq(n0,sK28(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_83])]) ).
fof(f898,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK28(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl40_33
| ~ spl40_83 ),
inference(forward_demodulation,[],[f896,f613]) ).
fof(f896,plain,
( ! [X0,X1] :
( leq(n0,sK28(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl40_83 ),
inference(avatar_component_clause,[],[f895]) ).
fof(f1096,plain,
( spl40_129
| ~ spl40_33
| ~ spl40_81 ),
inference(avatar_split_clause,[],[f889,f886,f611,f1094]) ).
fof(f1094,plain,
( spl40_129
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK27(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_129])]) ).
fof(f886,plain,
( spl40_81
<=> ! [X0,X1] :
( leq(n0,sK27(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_81])]) ).
fof(f889,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK27(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl40_33
| ~ spl40_81 ),
inference(forward_demodulation,[],[f887,f613]) ).
fof(f887,plain,
( ! [X0,X1] :
( leq(n0,sK27(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl40_81 ),
inference(avatar_component_clause,[],[f886]) ).
fof(f1092,plain,
( spl40_128
| ~ spl40_33
| ~ spl40_79 ),
inference(avatar_split_clause,[],[f880,f877,f611,f1090]) ).
fof(f1090,plain,
( spl40_128
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK26(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_128])]) ).
fof(f877,plain,
( spl40_79
<=> ! [X0,X1] :
( leq(n0,sK26(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_79])]) ).
fof(f880,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK26(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl40_33
| ~ spl40_79 ),
inference(forward_demodulation,[],[f878,f613]) ).
fof(f878,plain,
( ! [X0,X1] :
( leq(n0,sK26(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl40_79 ),
inference(avatar_component_clause,[],[f877]) ).
fof(f1088,plain,
( spl40_127
| ~ spl40_33
| ~ spl40_77 ),
inference(avatar_split_clause,[],[f871,f868,f611,f1086]) ).
fof(f1086,plain,
( spl40_127
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK25(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_127])]) ).
fof(f868,plain,
( spl40_77
<=> ! [X0,X1] :
( leq(n0,sK25(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_77])]) ).
fof(f871,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK25(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl40_33
| ~ spl40_77 ),
inference(forward_demodulation,[],[f869,f613]) ).
fof(f869,plain,
( ! [X0,X1] :
( leq(n0,sK25(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl40_77 ),
inference(avatar_component_clause,[],[f868]) ).
fof(f1084,plain,
( spl40_126
| ~ spl40_7
| ~ spl40_35 ),
inference(avatar_split_clause,[],[f648,f628,f478,f1081]) ).
fof(f1081,plain,
( spl40_126
<=> leq(tptp_minus_1,n3) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_126])]) ).
fof(f478,plain,
( spl40_7
<=> gt(n3,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_7])]) ).
fof(f648,plain,
( leq(tptp_minus_1,n3)
| ~ spl40_7
| ~ spl40_35 ),
inference(resolution,[],[f629,f480]) ).
fof(f480,plain,
( gt(n3,tptp_minus_1)
| ~ spl40_7 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f1079,plain,
( spl40_125
| ~ spl40_33
| ~ spl40_75 ),
inference(avatar_split_clause,[],[f862,f859,f611,f1077]) ).
fof(f1077,plain,
( spl40_125
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK24(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_125])]) ).
fof(f859,plain,
( spl40_75
<=> ! [X0,X1] :
( leq(n0,sK24(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_75])]) ).
fof(f862,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK24(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl40_33
| ~ spl40_75 ),
inference(forward_demodulation,[],[f860,f613]) ).
fof(f860,plain,
( ! [X0,X1] :
( leq(n0,sK24(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl40_75 ),
inference(avatar_component_clause,[],[f859]) ).
fof(f1075,plain,
( spl40_124
| ~ spl40_33
| ~ spl40_72 ),
inference(avatar_split_clause,[],[f848,f845,f611,f1073]) ).
fof(f1073,plain,
( spl40_124
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK23(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_124])]) ).
fof(f845,plain,
( spl40_72
<=> ! [X0,X1] :
( leq(n0,sK23(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_72])]) ).
fof(f848,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK23(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl40_33
| ~ spl40_72 ),
inference(forward_demodulation,[],[f846,f613]) ).
fof(f846,plain,
( ! [X0,X1] :
( leq(n0,sK23(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl40_72 ),
inference(avatar_component_clause,[],[f845]) ).
fof(f1071,plain,
( spl40_123
| ~ spl40_33
| ~ spl40_70 ),
inference(avatar_split_clause,[],[f839,f836,f611,f1069]) ).
fof(f1069,plain,
( spl40_123
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK22(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_123])]) ).
fof(f836,plain,
( spl40_70
<=> ! [X0,X1] :
( leq(n0,sK22(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_70])]) ).
fof(f839,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK22(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl40_33
| ~ spl40_70 ),
inference(forward_demodulation,[],[f837,f613]) ).
fof(f837,plain,
( ! [X0,X1] :
( leq(n0,sK22(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl40_70 ),
inference(avatar_component_clause,[],[f836]) ).
fof(f1067,plain,
( spl40_122
| ~ spl40_33
| ~ spl40_68 ),
inference(avatar_split_clause,[],[f830,f827,f611,f1065]) ).
fof(f1065,plain,
( spl40_122
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK21(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_122])]) ).
fof(f827,plain,
( spl40_68
<=> ! [X0,X1] :
( leq(n0,sK21(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_68])]) ).
fof(f830,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK21(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl40_33
| ~ spl40_68 ),
inference(forward_demodulation,[],[f828,f613]) ).
fof(f828,plain,
( ! [X0,X1] :
( leq(n0,sK21(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl40_68 ),
inference(avatar_component_clause,[],[f827]) ).
fof(f1063,plain,
( spl40_121
| ~ spl40_33
| ~ spl40_66 ),
inference(avatar_split_clause,[],[f821,f818,f611,f1061]) ).
fof(f1061,plain,
( spl40_121
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK20(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_121])]) ).
fof(f818,plain,
( spl40_66
<=> ! [X0,X1] :
( leq(n0,sK20(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_66])]) ).
fof(f821,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK20(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl40_33
| ~ spl40_66 ),
inference(forward_demodulation,[],[f819,f613]) ).
fof(f819,plain,
( ! [X0,X1] :
( leq(n0,sK20(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl40_66 ),
inference(avatar_component_clause,[],[f818]) ).
fof(f1059,plain,
( spl40_120
| ~ spl40_12
| ~ spl40_35 ),
inference(avatar_split_clause,[],[f645,f628,f503,f1056]) ).
fof(f1056,plain,
( spl40_120
<=> leq(n1,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_120])]) ).
fof(f503,plain,
( spl40_12
<=> gt(n2,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_12])]) ).
fof(f645,plain,
( leq(n1,n2)
| ~ spl40_12
| ~ spl40_35 ),
inference(resolution,[],[f629,f505]) ).
fof(f505,plain,
( gt(n2,n1)
| ~ spl40_12 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f1054,plain,
( spl40_119
| ~ spl40_33
| ~ spl40_64 ),
inference(avatar_split_clause,[],[f812,f809,f611,f1052]) ).
fof(f1052,plain,
( spl40_119
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK19(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_119])]) ).
fof(f809,plain,
( spl40_64
<=> ! [X0,X1] :
( leq(n0,sK19(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_64])]) ).
fof(f812,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK19(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl40_33
| ~ spl40_64 ),
inference(forward_demodulation,[],[f810,f613]) ).
fof(f810,plain,
( ! [X0,X1] :
( leq(n0,sK19(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl40_64 ),
inference(avatar_component_clause,[],[f809]) ).
fof(f1050,plain,
( spl40_118
| ~ spl40_33
| ~ spl40_60 ),
inference(avatar_split_clause,[],[f794,f791,f611,f1048]) ).
fof(f1048,plain,
( spl40_118
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK18(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_118])]) ).
fof(f791,plain,
( spl40_60
<=> ! [X0,X1] :
( leq(n0,sK18(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_60])]) ).
fof(f794,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK18(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl40_33
| ~ spl40_60 ),
inference(forward_demodulation,[],[f792,f613]) ).
fof(f792,plain,
( ! [X0,X1] :
( leq(n0,sK18(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl40_60 ),
inference(avatar_component_clause,[],[f791]) ).
fof(f1046,plain,
( spl40_117
| ~ spl40_33
| ~ spl40_58 ),
inference(avatar_split_clause,[],[f785,f782,f611,f1044]) ).
fof(f1044,plain,
( spl40_117
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK17(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_117])]) ).
fof(f782,plain,
( spl40_58
<=> ! [X0,X1] :
( leq(n0,sK17(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_58])]) ).
fof(f785,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK17(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl40_33
| ~ spl40_58 ),
inference(forward_demodulation,[],[f783,f613]) ).
fof(f783,plain,
( ! [X0,X1] :
( leq(n0,sK17(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl40_58 ),
inference(avatar_component_clause,[],[f782]) ).
fof(f1042,plain,
( spl40_116
| ~ spl40_33
| ~ spl40_56 ),
inference(avatar_split_clause,[],[f776,f773,f611,f1040]) ).
fof(f1040,plain,
( spl40_116
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK16(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_116])]) ).
fof(f773,plain,
( spl40_56
<=> ! [X0,X1] :
( leq(n0,sK16(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_56])]) ).
fof(f776,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK16(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl40_33
| ~ spl40_56 ),
inference(forward_demodulation,[],[f774,f613]) ).
fof(f774,plain,
( ! [X0,X1] :
( leq(n0,sK16(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl40_56 ),
inference(avatar_component_clause,[],[f773]) ).
fof(f1038,plain,
( spl40_115
| ~ spl40_33
| ~ spl40_54 ),
inference(avatar_split_clause,[],[f767,f764,f611,f1036]) ).
fof(f1036,plain,
( spl40_115
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK15(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_115])]) ).
fof(f764,plain,
( spl40_54
<=> ! [X0,X1] :
( leq(n0,sK15(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_54])]) ).
fof(f767,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK15(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl40_33
| ~ spl40_54 ),
inference(forward_demodulation,[],[f765,f613]) ).
fof(f765,plain,
( ! [X0,X1] :
( leq(n0,sK15(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl40_54 ),
inference(avatar_component_clause,[],[f764]) ).
fof(f1034,plain,
( spl40_114
| ~ spl40_11
| ~ spl40_35 ),
inference(avatar_split_clause,[],[f644,f628,f498,f1031]) ).
fof(f1031,plain,
( spl40_114
<=> leq(tptp_minus_1,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_114])]) ).
fof(f498,plain,
( spl40_11
<=> gt(n2,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_11])]) ).
fof(f644,plain,
( leq(tptp_minus_1,n2)
| ~ spl40_11
| ~ spl40_35 ),
inference(resolution,[],[f629,f500]) ).
fof(f500,plain,
( gt(n2,tptp_minus_1)
| ~ spl40_11 ),
inference(avatar_component_clause,[],[f498]) ).
fof(f1029,plain,
( spl40_113
| ~ spl40_33
| ~ spl40_52 ),
inference(avatar_split_clause,[],[f758,f755,f611,f1027]) ).
fof(f1027,plain,
( spl40_113
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK14(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_113])]) ).
fof(f755,plain,
( spl40_52
<=> ! [X0,X1] :
( leq(n0,sK14(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_52])]) ).
fof(f758,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK14(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl40_33
| ~ spl40_52 ),
inference(forward_demodulation,[],[f756,f613]) ).
fof(f756,plain,
( ! [X0,X1] :
( leq(n0,sK14(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl40_52 ),
inference(avatar_component_clause,[],[f755]) ).
fof(f1025,plain,
( spl40_112
| ~ spl40_33
| ~ spl40_49 ),
inference(avatar_split_clause,[],[f744,f741,f611,f1023]) ).
fof(f1023,plain,
( spl40_112
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK13(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_112])]) ).
fof(f741,plain,
( spl40_49
<=> ! [X0,X1] :
( leq(n0,sK13(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_49])]) ).
fof(f744,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK13(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl40_33
| ~ spl40_49 ),
inference(forward_demodulation,[],[f742,f613]) ).
fof(f742,plain,
( ! [X0,X1] :
( leq(n0,sK13(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl40_49 ),
inference(avatar_component_clause,[],[f741]) ).
fof(f1021,plain,
( spl40_111
| ~ spl40_33
| ~ spl40_48 ),
inference(avatar_split_clause,[],[f739,f736,f611,f1019]) ).
fof(f1019,plain,
( spl40_111
<=> ! [X0,X1] :
( leq(tptp_float_0_0,X1)
| ~ leq(minus(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_111])]) ).
fof(f736,plain,
( spl40_48
<=> ! [X0,X1] :
( leq(n0,X1)
| ~ leq(minus(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_48])]) ).
fof(f739,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,X1)
| ~ leq(minus(X0,X1),X0) )
| ~ spl40_33
| ~ spl40_48 ),
inference(forward_demodulation,[],[f737,f613]) ).
fof(f737,plain,
( ! [X0,X1] :
( leq(n0,X1)
| ~ leq(minus(X0,X1),X0) )
| ~ spl40_48 ),
inference(avatar_component_clause,[],[f736]) ).
fof(f1017,plain,
( spl40_110
| ~ spl40_33
| ~ spl40_47 ),
inference(avatar_split_clause,[],[f734,f731,f611,f1015]) ).
fof(f1015,plain,
( spl40_110
<=> ! [X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| leq(uniform_int_rnd(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_110])]) ).
fof(f731,plain,
( spl40_47
<=> ! [X0,X1] :
( leq(uniform_int_rnd(X1,X0),X0)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_47])]) ).
fof(f734,plain,
( ! [X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| leq(uniform_int_rnd(X1,X0),X0) )
| ~ spl40_33
| ~ spl40_47 ),
inference(forward_demodulation,[],[f732,f613]) ).
fof(f732,plain,
( ! [X0,X1] :
( leq(uniform_int_rnd(X1,X0),X0)
| ~ leq(n0,X0) )
| ~ spl40_47 ),
inference(avatar_component_clause,[],[f731]) ).
fof(f1013,plain,
( spl40_109
| ~ spl40_33
| ~ spl40_46 ),
inference(avatar_split_clause,[],[f729,f725,f611,f1011]) ).
fof(f1011,plain,
( spl40_109
<=> ! [X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| leq(tptp_float_0_0,uniform_int_rnd(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_109])]) ).
fof(f725,plain,
( spl40_46
<=> ! [X0,X1] :
( leq(n0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_46])]) ).
fof(f729,plain,
( ! [X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| leq(tptp_float_0_0,uniform_int_rnd(X1,X0)) )
| ~ spl40_33
| ~ spl40_46 ),
inference(forward_demodulation,[],[f728,f613]) ).
fof(f728,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) )
| ~ spl40_33
| ~ spl40_46 ),
inference(forward_demodulation,[],[f726,f613]) ).
fof(f726,plain,
( ! [X0,X1] :
( leq(n0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) )
| ~ spl40_46 ),
inference(avatar_component_clause,[],[f725]) ).
fof(f1009,plain,
spl40_108,
inference(avatar_split_clause,[],[f423,f1007]) ).
fof(f1007,plain,
( spl40_108
<=> ! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,minus(X1,n1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_108])]) ).
fof(f423,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,minus(X1,n1)) ),
inference(definition_unfolding,[],[f329,f285]) ).
fof(f285,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_minus_1) ).
fof(f329,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,pred(X1)) ),
inference(cnf_transformation,[],[f197]) ).
fof(f197,plain,
! [X0,X1] :
( ( leq(X0,pred(X1))
| ~ gt(X1,X0) )
& ( gt(X1,X0)
| ~ leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt_pred) ).
fof(f1005,plain,
spl40_107,
inference(avatar_split_clause,[],[f422,f1003]) ).
fof(f1003,plain,
( spl40_107
<=> ! [X0,X1] :
( leq(X0,minus(X1,n1))
| ~ gt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_107])]) ).
fof(f422,plain,
! [X0,X1] :
( leq(X0,minus(X1,n1))
| ~ gt(X1,X0) ),
inference(definition_unfolding,[],[f330,f285]) ).
fof(f330,plain,
! [X0,X1] :
( leq(X0,pred(X1))
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f197]) ).
fof(f1001,plain,
spl40_106,
inference(avatar_split_clause,[],[f421,f999]) ).
fof(f999,plain,
( spl40_106
<=> ! [X0,X1] :
( gt(plus(X1,n1),X0)
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_106])]) ).
fof(f421,plain,
! [X0,X1] :
( gt(plus(X1,n1),X0)
| ~ leq(X0,X1) ),
inference(definition_unfolding,[],[f327,f283]) ).
fof(f327,plain,
! [X0,X1] :
( gt(succ(X1),X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f196]) ).
fof(f196,plain,
! [X0,X1] :
( ( leq(X0,X1)
| ~ gt(succ(X1),X0) )
& ( gt(succ(X1),X0)
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> gt(succ(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
fof(f997,plain,
( spl40_105
| ~ spl40_20
| ~ spl40_35 ),
inference(avatar_split_clause,[],[f641,f628,f543,f994]) ).
fof(f994,plain,
( spl40_105
<=> leq(tptp_minus_1,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_105])]) ).
fof(f543,plain,
( spl40_20
<=> gt(n1,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_20])]) ).
fof(f641,plain,
( leq(tptp_minus_1,n1)
| ~ spl40_20
| ~ spl40_35 ),
inference(resolution,[],[f629,f545]) ).
fof(f545,plain,
( gt(n1,tptp_minus_1)
| ~ spl40_20 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f992,plain,
spl40_104,
inference(avatar_split_clause,[],[f420,f990]) ).
fof(f990,plain,
( spl40_104
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ gt(plus(X1,n1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_104])]) ).
fof(f420,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(plus(X1,n1),X0) ),
inference(definition_unfolding,[],[f328,f283]) ).
fof(f328,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(succ(X1),X0) ),
inference(cnf_transformation,[],[f196]) ).
fof(f988,plain,
spl40_103,
inference(avatar_split_clause,[],[f419,f986]) ).
fof(f986,plain,
( spl40_103
<=> ! [X0,X1] :
( gt(X1,X0)
| ~ leq(plus(X0,n1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_103])]) ).
fof(f419,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(plus(X0,n1),X1) ),
inference(definition_unfolding,[],[f306,f283]) ).
fof(f306,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(succ(X0),X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(succ(X0),X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1] :
( leq(succ(X0),X1)
=> gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt) ).
fof(f984,plain,
spl40_102,
inference(avatar_split_clause,[],[f418,f982]) ).
fof(f982,plain,
( spl40_102
<=> ! [X0,X1] :
( leq(X0,plus(X1,n1))
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_102])]) ).
fof(f418,plain,
! [X0,X1] :
( leq(X0,plus(X1,n1))
| ~ leq(X0,X1) ),
inference(definition_unfolding,[],[f302,f283]) ).
fof(f302,plain,
! [X0,X1] :
( leq(X0,succ(X1))
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1] :
( leq(X0,succ(X1))
| ~ leq(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
=> leq(X0,succ(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ) ).
fof(f980,plain,
spl40_101,
inference(avatar_split_clause,[],[f397,f978]) ).
fof(f978,plain,
( spl40_101
<=> ! [X0,X1] :
( leq(sK39(X0,X1),X1)
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_101])]) ).
fof(f397,plain,
! [X0,X1] :
( leq(sK39(X0,X1),X1)
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f244]) ).
fof(f244,plain,
! [X0,X1] :
( ( a_select3(X0,sK38(X0,X1),sK39(X0,X1)) != a_select3(X0,sK39(X0,X1),sK38(X0,X1))
& leq(sK39(X0,X1),X1)
& leq(n0,sK39(X0,X1))
& leq(sK38(X0,X1),X1)
& leq(n0,sK38(X0,X1)) )
| ~ sP10(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39])],[f242,f243]) ).
fof(f243,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK38(X0,X1),sK39(X0,X1)) != a_select3(X0,sK39(X0,X1),sK38(X0,X1))
& leq(sK39(X0,X1),X1)
& leq(n0,sK39(X0,X1))
& leq(sK38(X0,X1),X1)
& leq(n0,sK38(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f242,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP10(X0,X1) ),
inference(rectify,[],[f241]) ).
fof(f241,plain,
! [X3,X7] :
( ? [X12,X13] :
( a_select3(X3,X12,X13) != a_select3(X3,X13,X12)
& leq(X13,X7)
& leq(n0,X13)
& leq(X12,X7)
& leq(n0,X12) )
| ~ sP10(X3,X7) ),
inference(nnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X3,X7] :
( ? [X12,X13] :
( a_select3(X3,X12,X13) != a_select3(X3,X13,X12)
& leq(X13,X7)
& leq(n0,X13)
& leq(X12,X7)
& leq(n0,X12) )
| ~ sP10(X3,X7) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f975,plain,
spl40_100,
inference(avatar_split_clause,[],[f396,f973]) ).
fof(f396,plain,
! [X0,X1] :
( leq(n0,sK39(X0,X1))
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f244]) ).
fof(f971,plain,
spl40_99,
inference(avatar_split_clause,[],[f395,f969]) ).
fof(f969,plain,
( spl40_99
<=> ! [X0,X1] :
( leq(sK38(X0,X1),X1)
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_99])]) ).
fof(f395,plain,
! [X0,X1] :
( leq(sK38(X0,X1),X1)
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f244]) ).
fof(f966,plain,
spl40_98,
inference(avatar_split_clause,[],[f394,f964]) ).
fof(f394,plain,
! [X0,X1] :
( leq(n0,sK38(X0,X1))
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f244]) ).
fof(f962,plain,
spl40_97,
inference(avatar_split_clause,[],[f392,f960]) ).
fof(f960,plain,
( spl40_97
<=> ! [X0,X1] :
( leq(sK37(X0,X1),X1)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_97])]) ).
fof(f392,plain,
! [X0,X1] :
( leq(sK37(X0,X1),X1)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0,X1] :
( ( a_select3(X0,sK36(X0,X1),sK37(X0,X1)) != a_select3(X0,sK37(X0,X1),sK36(X0,X1))
& leq(sK37(X0,X1),X1)
& leq(n0,sK37(X0,X1))
& leq(sK36(X0,X1),X1)
& leq(n0,sK36(X0,X1)) )
| ~ sP11(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36,sK37])],[f238,f239]) ).
fof(f239,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK36(X0,X1),sK37(X0,X1)) != a_select3(X0,sK37(X0,X1),sK36(X0,X1))
& leq(sK37(X0,X1),X1)
& leq(n0,sK37(X0,X1))
& leq(sK36(X0,X1),X1)
& leq(n0,sK36(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f238,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP11(X0,X1) ),
inference(rectify,[],[f237]) ).
fof(f237,plain,
! [X0,X6] :
( ? [X10,X11] :
( a_select3(X0,X10,X11) != a_select3(X0,X11,X10)
& leq(X11,X6)
& leq(n0,X11)
& leq(X10,X6)
& leq(n0,X10) )
| ~ sP11(X0,X6) ),
inference(nnf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0,X6] :
( ? [X10,X11] :
( a_select3(X0,X10,X11) != a_select3(X0,X11,X10)
& leq(X11,X6)
& leq(n0,X11)
& leq(X10,X6)
& leq(n0,X10) )
| ~ sP11(X0,X6) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f957,plain,
spl40_96,
inference(avatar_split_clause,[],[f391,f955]) ).
fof(f391,plain,
! [X0,X1] :
( leq(n0,sK37(X0,X1))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f953,plain,
spl40_95,
inference(avatar_split_clause,[],[f390,f951]) ).
fof(f951,plain,
( spl40_95
<=> ! [X0,X1] :
( leq(sK36(X0,X1),X1)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_95])]) ).
fof(f390,plain,
! [X0,X1] :
( leq(sK36(X0,X1),X1)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f947,plain,
spl40_94,
inference(avatar_split_clause,[],[f389,f945]) ).
fof(f389,plain,
! [X0,X1] :
( leq(n0,sK36(X0,X1))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f943,plain,
spl40_93,
inference(avatar_split_clause,[],[f387,f941]) ).
fof(f941,plain,
( spl40_93
<=> ! [X0,X1] :
( leq(sK35(X0,X1),X1)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_93])]) ).
fof(f387,plain,
! [X0,X1] :
( leq(sK35(X0,X1),X1)
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f236,plain,
! [X0,X1] :
( ( a_select3(X0,sK34(X0,X1),sK35(X0,X1)) != a_select3(X0,sK35(X0,X1),sK34(X0,X1))
& leq(sK35(X0,X1),X1)
& leq(n0,sK35(X0,X1))
& leq(sK34(X0,X1),X1)
& leq(n0,sK34(X0,X1)) )
| ~ sP12(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35])],[f234,f235]) ).
fof(f235,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK34(X0,X1),sK35(X0,X1)) != a_select3(X0,sK35(X0,X1),sK34(X0,X1))
& leq(sK35(X0,X1),X1)
& leq(n0,sK35(X0,X1))
& leq(sK34(X0,X1),X1)
& leq(n0,sK34(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f234,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP12(X0,X1) ),
inference(rectify,[],[f233]) ).
fof(f233,plain,
! [X5,X6] :
( ? [X8,X9] :
( a_select3(X5,X8,X9) != a_select3(X5,X9,X8)
& leq(X9,X6)
& leq(n0,X9)
& leq(X8,X6)
& leq(n0,X8) )
| ~ sP12(X5,X6) ),
inference(nnf_transformation,[],[f182]) ).
fof(f182,plain,
! [X5,X6] :
( ? [X8,X9] :
( a_select3(X5,X8,X9) != a_select3(X5,X9,X8)
& leq(X9,X6)
& leq(n0,X9)
& leq(X8,X6)
& leq(n0,X8) )
| ~ sP12(X5,X6) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f938,plain,
spl40_92,
inference(avatar_split_clause,[],[f386,f936]) ).
fof(f386,plain,
! [X0,X1] :
( leq(n0,sK35(X0,X1))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f934,plain,
spl40_91,
inference(avatar_split_clause,[],[f385,f932]) ).
fof(f932,plain,
( spl40_91
<=> ! [X0,X1] :
( leq(sK34(X0,X1),X1)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_91])]) ).
fof(f385,plain,
! [X0,X1] :
( leq(sK34(X0,X1),X1)
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f929,plain,
spl40_90,
inference(avatar_split_clause,[],[f384,f927]) ).
fof(f384,plain,
! [X0,X1] :
( leq(n0,sK34(X0,X1))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f925,plain,
spl40_89,
inference(avatar_split_clause,[],[f372,f923]) ).
fof(f923,plain,
( spl40_89
<=> ! [X0,X1] :
( leq(sK31(X0,X1),X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_89])]) ).
fof(f372,plain,
! [X0,X1] :
( leq(sK31(X0,X1),X1)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f227]) ).
fof(f227,plain,
! [X0,X1] :
( ( a_select3(X0,sK30(X0,X1),sK31(X0,X1)) != a_select3(X0,sK31(X0,X1),sK30(X0,X1))
& leq(sK31(X0,X1),X1)
& leq(n0,sK31(X0,X1))
& leq(sK30(X0,X1),X1)
& leq(n0,sK30(X0,X1)) )
| ~ sP8(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31])],[f225,f226]) ).
fof(f226,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK30(X0,X1),sK31(X0,X1)) != a_select3(X0,sK31(X0,X1),sK30(X0,X1))
& leq(sK31(X0,X1),X1)
& leq(n0,sK31(X0,X1))
& leq(sK30(X0,X1),X1)
& leq(n0,sK30(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f225,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP8(X0,X1) ),
inference(rectify,[],[f224]) ).
fof(f224,plain,
! [X1,X3] :
( ? [X4,X5] :
( a_select3(X1,X4,X5) != a_select3(X1,X5,X4)
& leq(X5,X3)
& leq(n0,X5)
& leq(X4,X3)
& leq(n0,X4) )
| ~ sP8(X1,X3) ),
inference(nnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X1,X3] :
( ? [X4,X5] :
( a_select3(X1,X4,X5) != a_select3(X1,X5,X4)
& leq(X5,X3)
& leq(n0,X5)
& leq(X4,X3)
& leq(n0,X4) )
| ~ sP8(X1,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f920,plain,
spl40_88,
inference(avatar_split_clause,[],[f371,f918]) ).
fof(f371,plain,
! [X0,X1] :
( leq(n0,sK31(X0,X1))
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f227]) ).
fof(f916,plain,
spl40_87,
inference(avatar_split_clause,[],[f370,f914]) ).
fof(f914,plain,
( spl40_87
<=> ! [X0,X1] :
( leq(sK30(X0,X1),X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_87])]) ).
fof(f370,plain,
! [X0,X1] :
( leq(sK30(X0,X1),X1)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f227]) ).
fof(f911,plain,
spl40_86,
inference(avatar_split_clause,[],[f369,f909]) ).
fof(f369,plain,
! [X0,X1] :
( leq(n0,sK30(X0,X1))
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f227]) ).
fof(f907,plain,
spl40_85,
inference(avatar_split_clause,[],[f361,f905]) ).
fof(f905,plain,
( spl40_85
<=> ! [X0,X1] :
( leq(sK28(X0,X1),X1)
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_85])]) ).
fof(f361,plain,
! [X0,X1] :
( leq(sK28(X0,X1),X1)
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f220]) ).
fof(f220,plain,
! [X0,X1] :
( ( a_select3(X0,sK27(X0,X1),sK28(X0,X1)) != a_select3(X0,sK28(X0,X1),sK27(X0,X1))
& leq(sK28(X0,X1),X1)
& leq(n0,sK28(X0,X1))
& leq(sK27(X0,X1),X1)
& leq(n0,sK27(X0,X1)) )
| ~ sP7(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28])],[f218,f219]) ).
fof(f219,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK27(X0,X1),sK28(X0,X1)) != a_select3(X0,sK28(X0,X1),sK27(X0,X1))
& leq(sK28(X0,X1),X1)
& leq(n0,sK28(X0,X1))
& leq(sK27(X0,X1),X1)
& leq(n0,sK27(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f218,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP7(X0,X1) ),
inference(rectify,[],[f217]) ).
fof(f217,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP7(X1,X2) ),
inference(nnf_transformation,[],[f174]) ).
fof(f174,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP7(X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f903,plain,
( spl40_84
| ~ spl40_22
| ~ spl40_33 ),
inference(avatar_split_clause,[],[f620,f611,f553,f900]) ).
fof(f900,plain,
( spl40_84
<=> gt(tptp_float_0_0,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_84])]) ).
fof(f620,plain,
( gt(tptp_float_0_0,tptp_minus_1)
| ~ spl40_22
| ~ spl40_33 ),
inference(superposition,[],[f555,f613]) ).
fof(f897,plain,
spl40_83,
inference(avatar_split_clause,[],[f360,f895]) ).
fof(f360,plain,
! [X0,X1] :
( leq(n0,sK28(X0,X1))
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f220]) ).
fof(f893,plain,
spl40_82,
inference(avatar_split_clause,[],[f359,f891]) ).
fof(f891,plain,
( spl40_82
<=> ! [X0,X1] :
( leq(sK27(X0,X1),X1)
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_82])]) ).
fof(f359,plain,
! [X0,X1] :
( leq(sK27(X0,X1),X1)
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f220]) ).
fof(f888,plain,
spl40_81,
inference(avatar_split_clause,[],[f358,f886]) ).
fof(f358,plain,
! [X0,X1] :
( leq(n0,sK27(X0,X1))
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f220]) ).
fof(f884,plain,
spl40_80,
inference(avatar_split_clause,[],[f355,f882]) ).
fof(f882,plain,
( spl40_80
<=> ! [X0,X1] :
( leq(sK26(X0,X1),X1)
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_80])]) ).
fof(f355,plain,
! [X0,X1] :
( leq(sK26(X0,X1),X1)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f215]) ).
fof(f215,plain,
! [X0,X1] :
( ( a_select3(X0,sK25(X0,X1),sK26(X0,X1)) != a_select3(X0,sK26(X0,X1),sK25(X0,X1))
& leq(sK26(X0,X1),X1)
& leq(n0,sK26(X0,X1))
& leq(sK25(X0,X1),X1)
& leq(n0,sK25(X0,X1)) )
| ~ sP5(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f213,f214]) ).
fof(f214,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK25(X0,X1),sK26(X0,X1)) != a_select3(X0,sK26(X0,X1),sK25(X0,X1))
& leq(sK26(X0,X1),X1)
& leq(n0,sK26(X0,X1))
& leq(sK25(X0,X1),X1)
& leq(n0,sK25(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f213,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP5(X0,X1) ),
inference(rectify,[],[f212]) ).
fof(f212,plain,
! [X0,X2] :
( ? [X5,X6] :
( a_select3(X0,X5,X6) != a_select3(X0,X6,X5)
& leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) )
| ~ sP5(X0,X2) ),
inference(nnf_transformation,[],[f171]) ).
fof(f171,plain,
! [X0,X2] :
( ? [X5,X6] :
( a_select3(X0,X5,X6) != a_select3(X0,X6,X5)
& leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) )
| ~ sP5(X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f879,plain,
spl40_79,
inference(avatar_split_clause,[],[f354,f877]) ).
fof(f354,plain,
! [X0,X1] :
( leq(n0,sK26(X0,X1))
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f215]) ).
fof(f875,plain,
spl40_78,
inference(avatar_split_clause,[],[f353,f873]) ).
fof(f873,plain,
( spl40_78
<=> ! [X0,X1] :
( leq(sK25(X0,X1),X1)
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_78])]) ).
fof(f353,plain,
! [X0,X1] :
( leq(sK25(X0,X1),X1)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f215]) ).
fof(f870,plain,
spl40_77,
inference(avatar_split_clause,[],[f352,f868]) ).
fof(f352,plain,
! [X0,X1] :
( leq(n0,sK25(X0,X1))
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f215]) ).
fof(f866,plain,
spl40_76,
inference(avatar_split_clause,[],[f350,f864]) ).
fof(f864,plain,
( spl40_76
<=> ! [X0,X1] :
( leq(sK24(X0,X1),X1)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_76])]) ).
fof(f350,plain,
! [X0,X1] :
( leq(sK24(X0,X1),X1)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0,X1] :
( ( a_select3(X0,sK23(X0,X1),sK24(X0,X1)) != a_select3(X0,sK24(X0,X1),sK23(X0,X1))
& leq(sK24(X0,X1),X1)
& leq(n0,sK24(X0,X1))
& leq(sK23(X0,X1),X1)
& leq(n0,sK23(X0,X1)) )
| ~ sP6(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f209,f210]) ).
fof(f210,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK23(X0,X1),sK24(X0,X1)) != a_select3(X0,sK24(X0,X1),sK23(X0,X1))
& leq(sK24(X0,X1),X1)
& leq(n0,sK24(X0,X1))
& leq(sK23(X0,X1),X1)
& leq(n0,sK23(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f209,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP6(X0,X1) ),
inference(rectify,[],[f208]) ).
fof(f208,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP6(X1,X2) ),
inference(nnf_transformation,[],[f172]) ).
fof(f172,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP6(X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f861,plain,
spl40_75,
inference(avatar_split_clause,[],[f349,f859]) ).
fof(f349,plain,
! [X0,X1] :
( leq(n0,sK24(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f211]) ).
fof(f857,plain,
spl40_74,
inference(avatar_split_clause,[],[f348,f855]) ).
fof(f855,plain,
( spl40_74
<=> ! [X0,X1] :
( leq(sK23(X0,X1),X1)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_74])]) ).
fof(f348,plain,
! [X0,X1] :
( leq(sK23(X0,X1),X1)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f211]) ).
fof(f853,plain,
( spl40_73
| ~ spl40_21
| ~ spl40_33 ),
inference(avatar_split_clause,[],[f619,f611,f548,f850]) ).
fof(f850,plain,
( spl40_73
<=> gt(n1,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_73])]) ).
fof(f548,plain,
( spl40_21
<=> gt(n1,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_21])]) ).
fof(f619,plain,
( gt(n1,tptp_float_0_0)
| ~ spl40_21
| ~ spl40_33 ),
inference(superposition,[],[f550,f613]) ).
fof(f550,plain,
( gt(n1,n0)
| ~ spl40_21 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f847,plain,
spl40_72,
inference(avatar_split_clause,[],[f347,f845]) ).
fof(f347,plain,
! [X0,X1] :
( leq(n0,sK23(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f211]) ).
fof(f843,plain,
spl40_71,
inference(avatar_split_clause,[],[f344,f841]) ).
fof(f841,plain,
( spl40_71
<=> ! [X0,X1] :
( leq(sK22(X0,X1),X1)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_71])]) ).
fof(f344,plain,
! [X0,X1] :
( leq(sK22(X0,X1),X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f206]) ).
fof(f206,plain,
! [X0,X1] :
( ( a_select3(X0,sK21(X0,X1),sK22(X0,X1)) != a_select3(X0,sK22(X0,X1),sK21(X0,X1))
& leq(sK22(X0,X1),X1)
& leq(n0,sK22(X0,X1))
& leq(sK21(X0,X1),X1)
& leq(n0,sK21(X0,X1)) )
| ~ sP3(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f204,f205]) ).
fof(f205,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK21(X0,X1),sK22(X0,X1)) != a_select3(X0,sK22(X0,X1),sK21(X0,X1))
& leq(sK22(X0,X1),X1)
& leq(n0,sK22(X0,X1))
& leq(sK21(X0,X1),X1)
& leq(n0,sK21(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f204,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f203]) ).
fof(f203,plain,
! [X0,X2] :
( ? [X5,X6] :
( a_select3(X0,X5,X6) != a_select3(X0,X6,X5)
& leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) )
| ~ sP3(X0,X2) ),
inference(nnf_transformation,[],[f168]) ).
fof(f168,plain,
! [X0,X2] :
( ? [X5,X6] :
( a_select3(X0,X5,X6) != a_select3(X0,X6,X5)
& leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) )
| ~ sP3(X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f838,plain,
spl40_70,
inference(avatar_split_clause,[],[f343,f836]) ).
fof(f343,plain,
! [X0,X1] :
( leq(n0,sK22(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f206]) ).
fof(f834,plain,
spl40_69,
inference(avatar_split_clause,[],[f342,f832]) ).
fof(f832,plain,
( spl40_69
<=> ! [X0,X1] :
( leq(sK21(X0,X1),X1)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_69])]) ).
fof(f342,plain,
! [X0,X1] :
( leq(sK21(X0,X1),X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f206]) ).
fof(f829,plain,
spl40_68,
inference(avatar_split_clause,[],[f341,f827]) ).
fof(f341,plain,
! [X0,X1] :
( leq(n0,sK21(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f206]) ).
fof(f825,plain,
spl40_67,
inference(avatar_split_clause,[],[f339,f823]) ).
fof(f823,plain,
( spl40_67
<=> ! [X0,X1] :
( leq(sK20(X0,X1),X1)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_67])]) ).
fof(f339,plain,
! [X0,X1] :
( leq(sK20(X0,X1),X1)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0,X1] :
( ( a_select3(X0,sK19(X0,X1),sK20(X0,X1)) != a_select3(X0,sK20(X0,X1),sK19(X0,X1))
& leq(sK20(X0,X1),X1)
& leq(n0,sK20(X0,X1))
& leq(sK19(X0,X1),X1)
& leq(n0,sK19(X0,X1)) )
| ~ sP4(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f200,f201]) ).
fof(f201,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK19(X0,X1),sK20(X0,X1)) != a_select3(X0,sK20(X0,X1),sK19(X0,X1))
& leq(sK20(X0,X1),X1)
& leq(n0,sK20(X0,X1))
& leq(sK19(X0,X1),X1)
& leq(n0,sK19(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f200,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP4(X0,X1) ),
inference(rectify,[],[f199]) ).
fof(f199,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP4(X1,X2) ),
inference(nnf_transformation,[],[f169]) ).
fof(f169,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP4(X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f820,plain,
spl40_66,
inference(avatar_split_clause,[],[f338,f818]) ).
fof(f338,plain,
! [X0,X1] :
( leq(n0,sK20(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f202]) ).
fof(f816,plain,
spl40_65,
inference(avatar_split_clause,[],[f337,f814]) ).
fof(f814,plain,
( spl40_65
<=> ! [X0,X1] :
( leq(sK19(X0,X1),X1)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_65])]) ).
fof(f337,plain,
! [X0,X1] :
( leq(sK19(X0,X1),X1)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f202]) ).
fof(f811,plain,
spl40_64,
inference(avatar_split_clause,[],[f336,f809]) ).
fof(f336,plain,
! [X0,X1] :
( leq(n0,sK19(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f202]) ).
fof(f807,plain,
spl40_63,
inference(avatar_split_clause,[],[f333,f805]) ).
fof(f805,plain,
( spl40_63
<=> ! [X2,X0,X1] : a_select2(tptp_update2(X0,X1,X2),X1) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl40_63])]) ).
fof(f333,plain,
! [X2,X0,X1] : a_select2(tptp_update2(X0,X1,X2),X1) = X2,
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2] : a_select2(tptp_update2(X0,X1,X2),X1) = X2,
inference(rectify,[],[f48]) ).
fof(f48,axiom,
! [X0,X6,X16] : a_select2(tptp_update2(X0,X6,X16),X6) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel2_update_1) ).
fof(f803,plain,
( spl40_62
| ~ spl40_19
| ~ spl40_33 ),
inference(avatar_split_clause,[],[f618,f611,f538,f800]) ).
fof(f800,plain,
( spl40_62
<=> gt(n5,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_62])]) ).
fof(f538,plain,
( spl40_19
<=> gt(n5,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_19])]) ).
fof(f618,plain,
( gt(n5,tptp_float_0_0)
| ~ spl40_19
| ~ spl40_33 ),
inference(superposition,[],[f540,f613]) ).
fof(f540,plain,
( gt(n5,n0)
| ~ spl40_19 ),
inference(avatar_component_clause,[],[f538]) ).
fof(f798,plain,
spl40_61,
inference(avatar_split_clause,[],[f324,f796]) ).
fof(f796,plain,
( spl40_61
<=> ! [X0,X1] :
( leq(sK18(X0,X1),X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_61])]) ).
fof(f324,plain,
! [X0,X1] :
( leq(sK18(X0,X1),X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
! [X0,X1] :
( ( a_select3(X0,sK17(X0,X1),sK18(X0,X1)) != a_select3(X0,sK18(X0,X1),sK17(X0,X1))
& leq(sK18(X0,X1),X1)
& leq(n0,sK18(X0,X1))
& leq(sK17(X0,X1),X1)
& leq(n0,sK17(X0,X1)) )
| ~ sP2(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f192,f193]) ).
fof(f193,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK17(X0,X1),sK18(X0,X1)) != a_select3(X0,sK18(X0,X1),sK17(X0,X1))
& leq(sK18(X0,X1),X1)
& leq(n0,sK18(X0,X1))
& leq(sK17(X0,X1),X1)
& leq(n0,sK17(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f192,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP2(X0,X1) ),
inference(nnf_transformation,[],[f166]) ).
fof(f166,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP2(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f793,plain,
spl40_60,
inference(avatar_split_clause,[],[f323,f791]) ).
fof(f323,plain,
! [X0,X1] :
( leq(n0,sK18(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f789,plain,
spl40_59,
inference(avatar_split_clause,[],[f322,f787]) ).
fof(f787,plain,
( spl40_59
<=> ! [X0,X1] :
( leq(sK17(X0,X1),X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_59])]) ).
fof(f322,plain,
! [X0,X1] :
( leq(sK17(X0,X1),X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f784,plain,
spl40_58,
inference(avatar_split_clause,[],[f321,f782]) ).
fof(f321,plain,
! [X0,X1] :
( leq(n0,sK17(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f780,plain,
spl40_57,
inference(avatar_split_clause,[],[f318,f778]) ).
fof(f778,plain,
( spl40_57
<=> ! [X0,X1] :
( leq(sK16(X0,X1),X1)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_57])]) ).
fof(f318,plain,
! [X0,X1] :
( leq(sK16(X0,X1),X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f190]) ).
fof(f190,plain,
! [X0,X1] :
( ( a_select3(X0,sK15(X0,X1),sK16(X0,X1)) != a_select3(X0,sK16(X0,X1),sK15(X0,X1))
& leq(sK16(X0,X1),X1)
& leq(n0,sK16(X0,X1))
& leq(sK15(X0,X1),X1)
& leq(n0,sK15(X0,X1)) )
| ~ sP1(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f188,f189]) ).
fof(f189,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK15(X0,X1),sK16(X0,X1)) != a_select3(X0,sK16(X0,X1),sK15(X0,X1))
& leq(sK16(X0,X1),X1)
& leq(n0,sK16(X0,X1))
& leq(sK15(X0,X1),X1)
& leq(n0,sK15(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f188,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP1(X0,X1) ),
inference(nnf_transformation,[],[f164]) ).
fof(f164,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP1(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f775,plain,
spl40_56,
inference(avatar_split_clause,[],[f317,f773]) ).
fof(f317,plain,
! [X0,X1] :
( leq(n0,sK16(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f190]) ).
fof(f771,plain,
spl40_55,
inference(avatar_split_clause,[],[f316,f769]) ).
fof(f769,plain,
( spl40_55
<=> ! [X0,X1] :
( leq(sK15(X0,X1),X1)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_55])]) ).
fof(f316,plain,
! [X0,X1] :
( leq(sK15(X0,X1),X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f190]) ).
fof(f766,plain,
spl40_54,
inference(avatar_split_clause,[],[f315,f764]) ).
fof(f315,plain,
! [X0,X1] :
( leq(n0,sK15(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f190]) ).
fof(f762,plain,
spl40_53,
inference(avatar_split_clause,[],[f312,f760]) ).
fof(f760,plain,
( spl40_53
<=> ! [X0,X1] :
( leq(sK14(X0,X1),X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_53])]) ).
fof(f312,plain,
! [X0,X1] :
( leq(sK14(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0,X1] :
( ( a_select3(X0,sK13(X0,X1),sK14(X0,X1)) != a_select3(X0,sK14(X0,X1),sK13(X0,X1))
& leq(sK14(X0,X1),X1)
& leq(n0,sK14(X0,X1))
& leq(sK13(X0,X1),X1)
& leq(n0,sK13(X0,X1)) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f184,f185]) ).
fof(f185,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK13(X0,X1),sK14(X0,X1)) != a_select3(X0,sK14(X0,X1),sK13(X0,X1))
& leq(sK14(X0,X1),X1)
& leq(n0,sK14(X0,X1))
& leq(sK13(X0,X1),X1)
& leq(n0,sK13(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f184,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP0(X0,X1) ),
inference(nnf_transformation,[],[f162]) ).
fof(f162,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP0(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f757,plain,
spl40_52,
inference(avatar_split_clause,[],[f311,f755]) ).
fof(f311,plain,
! [X0,X1] :
( leq(n0,sK14(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f186]) ).
fof(f753,plain,
( spl40_51
| ~ spl40_13
| ~ spl40_33 ),
inference(avatar_split_clause,[],[f617,f611,f508,f750]) ).
fof(f750,plain,
( spl40_51
<=> gt(n2,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_51])]) ).
fof(f508,plain,
( spl40_13
<=> gt(n2,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_13])]) ).
fof(f617,plain,
( gt(n2,tptp_float_0_0)
| ~ spl40_13
| ~ spl40_33 ),
inference(superposition,[],[f510,f613]) ).
fof(f510,plain,
( gt(n2,n0)
| ~ spl40_13 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f748,plain,
spl40_50,
inference(avatar_split_clause,[],[f310,f746]) ).
fof(f746,plain,
( spl40_50
<=> ! [X0,X1] :
( leq(sK13(X0,X1),X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_50])]) ).
fof(f310,plain,
! [X0,X1] :
( leq(sK13(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f186]) ).
fof(f743,plain,
spl40_49,
inference(avatar_split_clause,[],[f309,f741]) ).
fof(f309,plain,
! [X0,X1] :
( leq(n0,sK13(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f186]) ).
fof(f738,plain,
spl40_48,
inference(avatar_split_clause,[],[f307,f736]) ).
fof(f307,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ leq(minus(X0,X1),X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ leq(minus(X0,X1),X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] :
( leq(minus(X0,X1),X0)
=> leq(n0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_minus) ).
fof(f733,plain,
spl40_47,
inference(avatar_split_clause,[],[f304,f731]) ).
fof(f304,plain,
! [X0,X1] :
( leq(uniform_int_rnd(X1,X0),X0)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0,X1] :
( leq(uniform_int_rnd(X1,X0),X0)
| ~ leq(n0,X0) ),
inference(ennf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( leq(n0,X0)
=> leq(uniform_int_rnd(X1,X0),X0) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X3] :
( leq(n0,X0)
=> leq(uniform_int_rnd(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniform_int_rand_ranges_hi) ).
fof(f727,plain,
spl40_46,
inference(avatar_split_clause,[],[f303,f725]) ).
fof(f303,plain,
! [X0,X1] :
( leq(n0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0,X1] :
( leq(n0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) ),
inference(ennf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( leq(n0,X0)
=> leq(n0,uniform_int_rnd(X1,X0)) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X0,X3] :
( leq(n0,X0)
=> leq(n0,uniform_int_rnd(X3,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniform_int_rand_ranges_lo) ).
fof(f706,plain,
spl40_45,
inference(avatar_split_clause,[],[f409,f704]) ).
fof(f704,plain,
( spl40_45
<=> ! [X0] : plus(X0,n1) = plus(n1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_45])]) ).
fof(f409,plain,
! [X0] : plus(X0,n1) = plus(n1,X0),
inference(definition_unfolding,[],[f284,f283]) ).
fof(f284,plain,
! [X0] : succ(X0) = plus(n1,X0),
inference(cnf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] : succ(X0) = plus(n1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_1_l) ).
fof(f702,plain,
spl40_44,
inference(avatar_split_clause,[],[f408,f700]) ).
fof(f700,plain,
( spl40_44
<=> ! [X0] : plus(minus(X0,n1),n1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl40_44])]) ).
fof(f408,plain,
! [X0] : plus(minus(X0,n1),n1) = X0,
inference(definition_unfolding,[],[f281,f283,f285]) ).
fof(f281,plain,
! [X0] : succ(pred(X0)) = X0,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] : succ(pred(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_pred) ).
fof(f698,plain,
( spl40_43
| ~ spl40_10
| ~ spl40_33 ),
inference(avatar_split_clause,[],[f616,f611,f493,f695]) ).
fof(f695,plain,
( spl40_43
<=> gt(n3,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_43])]) ).
fof(f493,plain,
( spl40_10
<=> gt(n3,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_10])]) ).
fof(f616,plain,
( gt(n3,tptp_float_0_0)
| ~ spl40_10
| ~ spl40_33 ),
inference(superposition,[],[f495,f613]) ).
fof(f495,plain,
( gt(n3,n0)
| ~ spl40_10 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f693,plain,
spl40_42,
inference(avatar_split_clause,[],[f407,f691]) ).
fof(f407,plain,
! [X0] : minus(plus(X0,n1),n1) = X0,
inference(definition_unfolding,[],[f280,f285,f283]) ).
fof(f280,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] : pred(succ(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_succ) ).
fof(f689,plain,
( spl40_41
| ~ spl40_33
| ~ spl40_39 ),
inference(avatar_split_clause,[],[f679,f675,f611,f686]) ).
fof(f686,plain,
( spl40_41
<=> pv88 = sum(tptp_float_0_0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_41])]) ).
fof(f679,plain,
( pv88 = sum(tptp_float_0_0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
| ~ spl40_33
| ~ spl40_39 ),
inference(forward_demodulation,[],[f677,f613]) ).
fof(f677,plain,
( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89)))))
| ~ spl40_39 ),
inference(avatar_component_clause,[],[f675]) ).
fof(f684,plain,
( spl40_40
| ~ spl40_33
| ~ spl40_38 ),
inference(avatar_split_clause,[],[f673,f669,f611,f681]) ).
fof(f681,plain,
( spl40_40
<=> pv86 = sum(tptp_float_0_0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_40])]) ).
fof(f673,plain,
( pv86 = sum(tptp_float_0_0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| ~ spl40_33
| ~ spl40_38 ),
inference(forward_demodulation,[],[f671,f613]) ).
fof(f671,plain,
( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| ~ spl40_38 ),
inference(avatar_component_clause,[],[f669]) ).
fof(f678,plain,
spl40_39,
inference(avatar_split_clause,[],[f247,f675]) ).
fof(f247,plain,
pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))),
inference(cnf_transformation,[],[f109]) ).
fof(f672,plain,
spl40_38,
inference(avatar_split_clause,[],[f246,f669]) ).
fof(f246,plain,
pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))),
inference(cnf_transformation,[],[f109]) ).
fof(f639,plain,
( spl40_37
| ~ spl40_33
| ~ spl40_34 ),
inference(avatar_split_clause,[],[f626,f623,f611,f637]) ).
fof(f623,plain,
( spl40_34
<=> ! [X0] : tptp_float_0_0 = sum(n0,tptp_minus_1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_34])]) ).
fof(f626,plain,
( ! [X0] : tptp_float_0_0 = sum(tptp_float_0_0,tptp_minus_1,X0)
| ~ spl40_33
| ~ spl40_34 ),
inference(forward_demodulation,[],[f624,f613]) ).
fof(f624,plain,
( ! [X0] : tptp_float_0_0 = sum(n0,tptp_minus_1,X0)
| ~ spl40_34 ),
inference(avatar_component_clause,[],[f623]) ).
fof(f635,plain,
( spl40_36
| ~ spl40_6
| ~ spl40_33 ),
inference(avatar_split_clause,[],[f615,f611,f473,f632]) ).
fof(f632,plain,
( spl40_36
<=> gt(n4,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_36])]) ).
fof(f473,plain,
( spl40_6
<=> gt(n4,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_6])]) ).
fof(f615,plain,
( gt(n4,tptp_float_0_0)
| ~ spl40_6
| ~ spl40_33 ),
inference(superposition,[],[f475,f613]) ).
fof(f475,plain,
( gt(n4,n0)
| ~ spl40_6 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f630,plain,
spl40_35,
inference(avatar_split_clause,[],[f305,f628]) ).
fof(f305,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( gt(X1,X0)
=> leq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt1) ).
fof(f625,plain,
spl40_34,
inference(avatar_split_clause,[],[f286,f623]) ).
fof(f286,plain,
! [X0] : tptp_float_0_0 = sum(n0,tptp_minus_1,X0),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0] : tptp_float_0_0 = sum(n0,tptp_minus_1,X0),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X22] : sum(n0,tptp_minus_1,X22) = tptp_float_0_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_plus_base_float) ).
fof(f614,plain,
( spl40_33
| ~ spl40_32 ),
inference(avatar_split_clause,[],[f609,f606,f611]) ).
fof(f606,plain,
( spl40_32
<=> ! [X0] : n0 = sum(n0,tptp_minus_1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_32])]) ).
fof(f609,plain,
( n0 = tptp_float_0_0
| ~ spl40_32 ),
inference(forward_demodulation,[],[f607,f286]) ).
fof(f607,plain,
( ! [X0] : n0 = sum(n0,tptp_minus_1,X0)
| ~ spl40_32 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f608,plain,
spl40_32,
inference(avatar_split_clause,[],[f282,f606]) ).
fof(f282,plain,
! [X0] : n0 = sum(n0,tptp_minus_1,X0),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0] : n0 = sum(n0,tptp_minus_1,X0),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X22] : n0 = sum(n0,tptp_minus_1,X22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_plus_base) ).
fof(f598,plain,
spl40_31,
inference(avatar_split_clause,[],[f438,f595]) ).
fof(f595,plain,
( spl40_31
<=> n5 = plus(n4,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_31])]) ).
fof(f438,plain,
n5 = plus(n4,n1),
inference(forward_demodulation,[],[f437,f434]) ).
fof(f434,plain,
n4 = plus(n3,n1),
inference(forward_demodulation,[],[f433,f431]) ).
fof(f431,plain,
n3 = plus(n2,n1),
inference(forward_demodulation,[],[f430,f429]) ).
fof(f429,plain,
n2 = plus(n1,n1),
inference(forward_demodulation,[],[f402,f400]) ).
fof(f400,plain,
n1 = plus(n0,n1),
inference(definition_unfolding,[],[f271,f283]) ).
fof(f271,plain,
n1 = succ(n0),
inference(cnf_transformation,[],[f84]) ).
fof(f84,axiom,
n1 = succ(n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
fof(f402,plain,
n2 = plus(plus(n0,n1),n1),
inference(definition_unfolding,[],[f273,f283,f283]) ).
fof(f273,plain,
n2 = succ(succ(n0)),
inference(cnf_transformation,[],[f85]) ).
fof(f85,axiom,
n2 = succ(succ(n0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_2) ).
fof(f430,plain,
n3 = plus(plus(n1,n1),n1),
inference(forward_demodulation,[],[f403,f400]) ).
fof(f403,plain,
n3 = plus(plus(plus(n0,n1),n1),n1),
inference(definition_unfolding,[],[f274,f283,f283,f283]) ).
fof(f274,plain,
n3 = succ(succ(succ(n0))),
inference(cnf_transformation,[],[f86]) ).
fof(f86,axiom,
n3 = succ(succ(succ(n0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_3) ).
fof(f433,plain,
n4 = plus(plus(n2,n1),n1),
inference(forward_demodulation,[],[f432,f429]) ).
fof(f432,plain,
n4 = plus(plus(plus(n1,n1),n1),n1),
inference(forward_demodulation,[],[f404,f400]) ).
fof(f404,plain,
n4 = plus(plus(plus(plus(n0,n1),n1),n1),n1),
inference(definition_unfolding,[],[f275,f283,f283,f283,f283]) ).
fof(f275,plain,
n4 = succ(succ(succ(succ(n0)))),
inference(cnf_transformation,[],[f82]) ).
fof(f82,axiom,
n4 = succ(succ(succ(succ(n0)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_4) ).
fof(f437,plain,
n5 = plus(plus(n3,n1),n1),
inference(forward_demodulation,[],[f436,f431]) ).
fof(f436,plain,
n5 = plus(plus(plus(n2,n1),n1),n1),
inference(forward_demodulation,[],[f435,f429]) ).
fof(f435,plain,
n5 = plus(plus(plus(plus(n1,n1),n1),n1),n1),
inference(forward_demodulation,[],[f405,f400]) ).
fof(f405,plain,
n5 = plus(plus(plus(plus(plus(n0,n1),n1),n1),n1),n1),
inference(definition_unfolding,[],[f276,f283,f283,f283,f283,f283]) ).
fof(f276,plain,
n5 = succ(succ(succ(succ(succ(n0))))),
inference(cnf_transformation,[],[f83]) ).
fof(f83,axiom,
n5 = succ(succ(succ(succ(succ(n0))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_5) ).
fof(f593,plain,
spl40_30,
inference(avatar_split_clause,[],[f434,f590]) ).
fof(f590,plain,
( spl40_30
<=> n4 = plus(n3,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_30])]) ).
fof(f588,plain,
spl40_29,
inference(avatar_split_clause,[],[f431,f585]) ).
fof(f585,plain,
( spl40_29
<=> n3 = plus(n2,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_29])]) ).
fof(f583,plain,
spl40_28,
inference(avatar_split_clause,[],[f429,f580]) ).
fof(f580,plain,
( spl40_28
<=> n2 = plus(n1,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_28])]) ).
fof(f578,plain,
spl40_27,
inference(avatar_split_clause,[],[f406,f576]) ).
fof(f576,plain,
( spl40_27
<=> ! [X0] : gt(plus(X0,n1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_27])]) ).
fof(f406,plain,
! [X0] : gt(plus(X0,n1),X0),
inference(definition_unfolding,[],[f279,f283]) ).
fof(f279,plain,
! [X0] : gt(succ(X0),X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : gt(succ(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_succ) ).
fof(f574,plain,
spl40_26,
inference(avatar_split_clause,[],[f401,f571]) ).
fof(f401,plain,
n0 = plus(tptp_minus_1,n1),
inference(definition_unfolding,[],[f272,f283]) ).
fof(f272,plain,
n0 = succ(tptp_minus_1),
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
n0 = succ(tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
fof(f569,plain,
spl40_25,
inference(avatar_split_clause,[],[f400,f566]) ).
fof(f566,plain,
( spl40_25
<=> n1 = plus(n0,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_25])]) ).
fof(f564,plain,
spl40_24,
inference(avatar_split_clause,[],[f278,f562]) ).
fof(f562,plain,
( spl40_24
<=> ! [X0] : leq(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_24])]) ).
fof(f278,plain,
! [X0] : leq(X0,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : leq(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_leq) ).
fof(f560,plain,
spl40_23,
inference(avatar_split_clause,[],[f277,f558]) ).
fof(f558,plain,
( spl40_23
<=> ! [X0] : ~ gt(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl40_23])]) ).
fof(f277,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_gt) ).
fof(f556,plain,
spl40_22,
inference(avatar_split_clause,[],[f270,f553]) ).
fof(f270,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[],[f58]) ).
fof(f58,axiom,
gt(n0,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
fof(f551,plain,
spl40_21,
inference(avatar_split_clause,[],[f269,f548]) ).
fof(f269,plain,
gt(n1,n0),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
gt(n1,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_0) ).
fof(f546,plain,
spl40_20,
inference(avatar_split_clause,[],[f268,f543]) ).
fof(f268,plain,
gt(n1,tptp_minus_1),
inference(cnf_transformation,[],[f59]) ).
fof(f59,axiom,
gt(n1,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_tptp_minus_1) ).
fof(f541,plain,
spl40_19,
inference(avatar_split_clause,[],[f267,f538]) ).
fof(f267,plain,
gt(n5,n0),
inference(cnf_transformation,[],[f63]) ).
fof(f63,axiom,
gt(n5,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_0) ).
fof(f536,plain,
spl40_18,
inference(avatar_split_clause,[],[f266,f533]) ).
fof(f266,plain,
gt(n5,n1),
inference(cnf_transformation,[],[f68]) ).
fof(f68,axiom,
gt(n5,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_1) ).
fof(f531,plain,
spl40_17,
inference(avatar_split_clause,[],[f265,f528]) ).
fof(f265,plain,
gt(n5,n2),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
gt(n5,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_2) ).
fof(f526,plain,
spl40_16,
inference(avatar_split_clause,[],[f264,f523]) ).
fof(f264,plain,
gt(n5,n3),
inference(cnf_transformation,[],[f75]) ).
fof(f75,axiom,
gt(n5,n3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_3) ).
fof(f521,plain,
spl40_15,
inference(avatar_split_clause,[],[f263,f518]) ).
fof(f263,plain,
gt(n5,n4),
inference(cnf_transformation,[],[f55]) ).
fof(f55,axiom,
gt(n5,n4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_4) ).
fof(f516,plain,
spl40_14,
inference(avatar_split_clause,[],[f262,f513]) ).
fof(f262,plain,
gt(n5,tptp_minus_1),
inference(cnf_transformation,[],[f57]) ).
fof(f57,axiom,
gt(n5,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_tptp_minus_1) ).
fof(f511,plain,
spl40_13,
inference(avatar_split_clause,[],[f261,f508]) ).
fof(f261,plain,
gt(n2,n0),
inference(cnf_transformation,[],[f65]) ).
fof(f65,axiom,
gt(n2,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_0) ).
fof(f506,plain,
spl40_12,
inference(avatar_split_clause,[],[f260,f503]) ).
fof(f260,plain,
gt(n2,n1),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
gt(n2,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_1) ).
fof(f501,plain,
spl40_11,
inference(avatar_split_clause,[],[f259,f498]) ).
fof(f259,plain,
gt(n2,tptp_minus_1),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
gt(n2,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_tptp_minus_1) ).
fof(f496,plain,
spl40_10,
inference(avatar_split_clause,[],[f258,f493]) ).
fof(f258,plain,
gt(n3,n0),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
gt(n3,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_0) ).
fof(f491,plain,
spl40_9,
inference(avatar_split_clause,[],[f257,f488]) ).
fof(f257,plain,
gt(n3,n1),
inference(cnf_transformation,[],[f70]) ).
fof(f70,axiom,
gt(n3,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_1) ).
fof(f486,plain,
spl40_8,
inference(avatar_split_clause,[],[f256,f483]) ).
fof(f256,plain,
gt(n3,n2),
inference(cnf_transformation,[],[f73]) ).
fof(f73,axiom,
gt(n3,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_2) ).
fof(f481,plain,
spl40_7,
inference(avatar_split_clause,[],[f255,f478]) ).
fof(f255,plain,
gt(n3,tptp_minus_1),
inference(cnf_transformation,[],[f61]) ).
fof(f61,axiom,
gt(n3,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_tptp_minus_1) ).
fof(f476,plain,
spl40_6,
inference(avatar_split_clause,[],[f254,f473]) ).
fof(f254,plain,
gt(n4,n0),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
gt(n4,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_0) ).
fof(f471,plain,
spl40_5,
inference(avatar_split_clause,[],[f253,f468]) ).
fof(f253,plain,
gt(n4,n1),
inference(cnf_transformation,[],[f67]) ).
fof(f67,axiom,
gt(n4,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_1) ).
fof(f466,plain,
spl40_4,
inference(avatar_split_clause,[],[f252,f463]) ).
fof(f252,plain,
gt(n4,n2),
inference(cnf_transformation,[],[f71]) ).
fof(f71,axiom,
gt(n4,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_2) ).
fof(f461,plain,
spl40_3,
inference(avatar_split_clause,[],[f251,f458]) ).
fof(f251,plain,
gt(n4,n3),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
gt(n4,n3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_3) ).
fof(f456,plain,
spl40_2,
inference(avatar_split_clause,[],[f250,f453]) ).
fof(f250,plain,
gt(n4,tptp_minus_1),
inference(cnf_transformation,[],[f56]) ).
fof(f56,axiom,
gt(n4,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_tptp_minus_1) ).
fof(f451,plain,
~ spl40_1,
inference(avatar_split_clause,[],[f249,f448]) ).
fof(f448,plain,
( spl40_1
<=> def = use ),
introduced(avatar_definition,[new_symbols(naming,[spl40_1])]) ).
fof(f249,plain,
def != use,
inference(cnf_transformation,[],[f52]) ).
fof(f52,axiom,
def != use,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defuse) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV050+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 30 04:31:26 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % (29959)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (29966)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 % (29965)WARNING: value z3 for option sas not known
% 0.13/0.36 % (29963)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36 % (29964)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36 % (29967)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.36 % (29968)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.36 % (29965)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.36 % (29969)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.41 % (29967)First to succeed.
% 0.20/0.42 % (29967)Refutation found. Thanks to Tanya!
% 0.20/0.42 % SZS status Theorem for theBenchmark
% 0.20/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.43 % (29967)------------------------------
% 0.20/0.43 % (29967)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.43 % (29967)Termination reason: Refutation
% 0.20/0.43
% 0.20/0.43 % (29967)Memory used [KB]: 1976
% 0.20/0.43 % (29967)Time elapsed: 0.055 s
% 0.20/0.43 % (29967)Instructions burned: 99 (million)
% 0.20/0.43 % (29967)------------------------------
% 0.20/0.43 % (29967)------------------------------
% 0.20/0.43 % (29959)Success in time 0.078 s
%------------------------------------------------------------------------------