TSTP Solution File: NUM854+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM854+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n024.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 14:37:54 EDT 2024
% Result : Theorem 0.20s 0.38s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 98
% Syntax : Number of formulae : 300 ( 89 unt; 0 def)
% Number of atoms : 622 ( 144 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 534 ( 212 ~; 193 |; 25 &)
% ( 61 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 59 ( 57 usr; 54 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 523 ( 507 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f656,plain,
$false,
inference(avatar_sat_refutation,[],[f261,f266,f271,f275,f279,f283,f287,f291,f295,f299,f303,f307,f311,f315,f319,f323,f327,f331,f335,f339,f343,f359,f363,f367,f371,f395,f399,f409,f413,f417,f422,f426,f430,f434,f438,f442,f457,f468,f472,f476,f480,f484,f488,f492,f497,f501,f505,f509,f513,f517,f521,f554,f654,f655]) ).
fof(f655,plain,
( ~ spl4_2
| spl4_1
| ~ spl4_43 ),
inference(avatar_split_clause,[],[f569,f486,f258,f263]) ).
fof(f263,plain,
( spl4_2
<=> greater(vd508,vd509) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f258,plain,
( spl4_1
<=> greater(vmul(vd508,vd511),vmul(vd509,vd511)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f486,plain,
( spl4_43
<=> ! [X2,X0,X1] :
( greater(vmul(X1,X0),vmul(X2,X0))
| ~ greater(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_43])]) ).
fof(f569,plain,
( ~ greater(vd508,vd509)
| spl4_1
| ~ spl4_43 ),
inference(resolution,[],[f487,f260]) ).
fof(f260,plain,
( ~ greater(vmul(vd508,vd511),vmul(vd509,vd511))
| spl4_1 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f487,plain,
( ! [X2,X0,X1] :
( greater(vmul(X1,X0),vmul(X2,X0))
| ~ greater(X1,X2) )
| ~ spl4_43 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f654,plain,
spl4_53,
inference(avatar_split_clause,[],[f213,f652]) ).
fof(f652,plain,
( spl4_53
<=> ! [X2,X0,X1] : vmul(vmul(X0,X1),X2) = vmul(X0,vmul(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_53])]) ).
fof(f213,plain,
! [X2,X0,X1] : vmul(vmul(X0,X1),X2) = vmul(X0,vmul(X1,X2)),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2] : vmul(vmul(X0,X1),X2) = vmul(X0,vmul(X1,X2)),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X16,X17,X18] : vmul(vmul(X16,X17),X18) = vmul(X16,vmul(X17,X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(290, 0), 0)') ).
fof(f554,plain,
( spl4_52
| ~ spl4_3
| ~ spl4_21 ),
inference(avatar_split_clause,[],[f354,f341,f268,f551]) ).
fof(f551,plain,
( spl4_52
<=> geq(vd511,vd512) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_52])]) ).
fof(f268,plain,
( spl4_3
<=> greater(vd511,vd512) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
fof(f341,plain,
( spl4_21
<=> ! [X0,X1] :
( geq(X1,X0)
| ~ greater(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_21])]) ).
fof(f354,plain,
( geq(vd511,vd512)
| ~ spl4_3
| ~ spl4_21 ),
inference(resolution,[],[f342,f270]) ).
fof(f270,plain,
( greater(vd511,vd512)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f342,plain,
( ! [X0,X1] :
( ~ greater(X1,X0)
| geq(X1,X0) )
| ~ spl4_21 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f521,plain,
spl4_51,
inference(avatar_split_clause,[],[f227,f519]) ).
fof(f519,plain,
( spl4_51
<=> ! [X2,X0,X1] :
( greater(X0,X1)
| ~ greater(vplus(X0,X2),vplus(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_51])]) ).
fof(f227,plain,
! [X2,X0,X1] :
( greater(X0,X1)
| ~ greater(vplus(X0,X2),vplus(X1,X2)) ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0,X1,X2] :
( greater(X0,X1)
| ~ greater(vplus(X0,X2),vplus(X1,X2)) ),
inference(ennf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0,X1,X2] :
( greater(vplus(X0,X2),vplus(X1,X2))
=> greater(X0,X1) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X46,X47,X48] :
( greater(vplus(X46,X48),vplus(X47,X48))
=> greater(X46,X47) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
fof(f517,plain,
spl4_50,
inference(avatar_split_clause,[],[f226,f515]) ).
fof(f515,plain,
( spl4_50
<=> ! [X2,X0,X1] :
( greater(X0,X2)
| ~ greater(vmul(X0,X1),vmul(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_50])]) ).
fof(f226,plain,
! [X2,X0,X1] :
( greater(X0,X2)
| ~ greater(vmul(X0,X1),vmul(X2,X1)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(vmul(X0,X1),vmul(X2,X1)) ),
inference(ennf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1,X2] :
( greater(vmul(X0,X1),vmul(X2,X1))
=> greater(X0,X2) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X6,X7,X8] :
( greater(vmul(X6,X7),vmul(X8,X7))
=> greater(X6,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct1(307), 0), 0)') ).
fof(f513,plain,
spl4_49,
inference(avatar_split_clause,[],[f225,f511]) ).
fof(f511,plain,
( spl4_49
<=> ! [X2,X0,X1] :
( less(X0,X1)
| ~ less(vplus(X0,X2),vplus(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_49])]) ).
fof(f225,plain,
! [X2,X0,X1] :
( less(X0,X1)
| ~ less(vplus(X0,X2),vplus(X1,X2)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
! [X0,X1,X2] :
( less(X0,X1)
| ~ less(vplus(X0,X2),vplus(X1,X2)) ),
inference(ennf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0,X1,X2] :
( less(vplus(X0,X2),vplus(X1,X2))
=> less(X0,X1) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X46,X47,X48] :
( less(vplus(X46,X48),vplus(X47,X48))
=> less(X46,X47) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 0)') ).
fof(f509,plain,
spl4_48,
inference(avatar_split_clause,[],[f224,f507]) ).
fof(f507,plain,
( spl4_48
<=> ! [X2,X0,X1] :
( less(X0,X2)
| ~ less(vmul(X0,X1),vmul(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_48])]) ).
fof(f224,plain,
! [X2,X0,X1] :
( less(X0,X2)
| ~ less(vmul(X0,X1),vmul(X2,X1)) ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
! [X0,X1,X2] :
( less(X0,X2)
| ~ less(vmul(X0,X1),vmul(X2,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( less(vmul(X0,X1),vmul(X2,X1))
=> less(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct2(conjunct2(307)), 0), 0)') ).
fof(f505,plain,
spl4_47,
inference(avatar_split_clause,[],[f223,f503]) ).
fof(f503,plain,
( spl4_47
<=> ! [X2,X0,X1] :
( X0 = X1
| vplus(X0,X2) != vplus(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_47])]) ).
fof(f223,plain,
! [X2,X0,X1] :
( X0 = X1
| vplus(X0,X2) != vplus(X1,X2) ),
inference(cnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0,X1,X2] :
( X0 = X1
| vplus(X0,X2) != vplus(X1,X2) ),
inference(ennf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0,X1,X2] :
( vplus(X0,X2) = vplus(X1,X2)
=> X0 = X1 ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X46,X47,X48] :
( vplus(X46,X48) = vplus(X47,X48)
=> X46 = X47 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 1)') ).
fof(f501,plain,
spl4_46,
inference(avatar_split_clause,[],[f222,f499]) ).
fof(f499,plain,
( spl4_46
<=> ! [X2,X0,X1] :
( X0 = X2
| vmul(X0,X1) != vmul(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_46])]) ).
fof(f222,plain,
! [X2,X0,X1] :
( X0 = X2
| vmul(X0,X1) != vmul(X2,X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0,X1,X2] :
( X0 = X2
| vmul(X0,X1) != vmul(X2,X1) ),
inference(ennf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1,X2] :
( vmul(X0,X1) = vmul(X2,X1)
=> X0 = X2 ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X3,X4,X5] :
( vmul(X3,X4) = vmul(X5,X4)
=> X3 = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct1(conjunct2(307)), 0), 0)') ).
fof(f497,plain,
( spl4_45
| ~ spl4_2
| ~ spl4_21 ),
inference(avatar_split_clause,[],[f353,f341,f263,f494]) ).
fof(f494,plain,
( spl4_45
<=> geq(vd508,vd509) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_45])]) ).
fof(f353,plain,
( geq(vd508,vd509)
| ~ spl4_2
| ~ spl4_21 ),
inference(resolution,[],[f342,f265]) ).
fof(f265,plain,
( greater(vd508,vd509)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f492,plain,
spl4_44,
inference(avatar_split_clause,[],[f221,f490]) ).
fof(f490,plain,
( spl4_44
<=> ! [X2,X0,X1] :
( greater(vplus(X0,X2),vplus(X1,X2))
| ~ greater(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_44])]) ).
fof(f221,plain,
! [X2,X0,X1] :
( greater(vplus(X0,X2),vplus(X1,X2))
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0,X1,X2] :
( greater(vplus(X0,X2),vplus(X1,X2))
| ~ greater(X0,X1) ),
inference(ennf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1,X2] :
( greater(X0,X1)
=> greater(vplus(X0,X2),vplus(X1,X2)) ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X49,X50,X51] :
( greater(X49,X50)
=> greater(vplus(X49,X51),vplus(X50,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
fof(f488,plain,
spl4_43,
inference(avatar_split_clause,[],[f220,f486]) ).
fof(f220,plain,
! [X2,X0,X1] :
( greater(vmul(X1,X0),vmul(X2,X0))
| ~ greater(X1,X2) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0,X1,X2] :
( greater(vmul(X1,X0),vmul(X2,X0))
| ~ greater(X1,X2) ),
inference(ennf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2] :
( greater(X1,X2)
=> greater(vmul(X1,X0),vmul(X2,X0)) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X9,X14,X15] :
( greater(X14,X15)
=> greater(vmul(X14,X9),vmul(X15,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 2)') ).
fof(f484,plain,
spl4_42,
inference(avatar_split_clause,[],[f219,f482]) ).
fof(f482,plain,
( spl4_42
<=> ! [X2,X0,X1] :
( less(vplus(X0,X2),vplus(X1,X2))
| ~ less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_42])]) ).
fof(f219,plain,
! [X2,X0,X1] :
( less(vplus(X0,X2),vplus(X1,X2))
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0,X1,X2] :
( less(vplus(X0,X2),vplus(X1,X2))
| ~ less(X0,X1) ),
inference(ennf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1,X2] :
( less(X0,X1)
=> less(vplus(X0,X2),vplus(X1,X2)) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X49,X50,X51] :
( less(X49,X50)
=> less(vplus(X49,X51),vplus(X50,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 0)') ).
fof(f480,plain,
spl4_41,
inference(avatar_split_clause,[],[f218,f478]) ).
fof(f478,plain,
( spl4_41
<=> ! [X2,X0,X1] :
( less(vmul(X1,X0),vmul(X2,X0))
| ~ less(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_41])]) ).
fof(f218,plain,
! [X2,X0,X1] :
( less(vmul(X1,X0),vmul(X2,X0))
| ~ less(X1,X2) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0,X1,X2] :
( less(vmul(X1,X0),vmul(X2,X0))
| ~ less(X1,X2) ),
inference(ennf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2] :
( less(X1,X2)
=> less(vmul(X1,X0),vmul(X2,X0)) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X9,X10,X11] :
( less(X10,X11)
=> less(vmul(X10,X9),vmul(X11,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 0)') ).
fof(f476,plain,
spl4_40,
inference(avatar_split_clause,[],[f211,f474]) ).
fof(f474,plain,
( spl4_40
<=> ! [X0,X1] :
( vplus(X0,sK3(X0,X1)) = X1
| ~ greater(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_40])]) ).
fof(f211,plain,
! [X0,X1] :
( vplus(X0,sK3(X0,X1)) = X1
| ~ greater(X1,X0) ),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( vplus(X0,sK3(X0,X1)) = X1
| ~ greater(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f164,f165]) ).
fof(f165,plain,
! [X0,X1] :
( ? [X3] : vplus(X0,X3) = X1
=> vplus(X0,sK3(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f164,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X3] : vplus(X0,X3) = X1
| ~ greater(X1,X0) ) ),
inference(rectify,[],[f163]) ).
fof(f163,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X2] : vplus(X0,X2) = X1
| ~ greater(X1,X0) ) ),
inference(nnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1] :
( greater(X1,X0)
<=> ? [X2] : vplus(X0,X2) = X1 ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X80,X81] :
( greater(X81,X80)
<=> ? [X82] : vplus(X80,X82) = X81 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof(f472,plain,
spl4_39,
inference(avatar_split_clause,[],[f209,f470]) ).
fof(f470,plain,
( spl4_39
<=> ! [X0,X1] :
( vplus(X1,sK2(X0,X1)) = X0
| ~ less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_39])]) ).
fof(f209,plain,
! [X0,X1] :
( vplus(X1,sK2(X0,X1)) = X0
| ~ less(X1,X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( vplus(X1,sK2(X0,X1)) = X0
| ~ less(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f160,f161]) ).
fof(f161,plain,
! [X0,X1] :
( ? [X3] : vplus(X1,X3) = X0
=> vplus(X1,sK2(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f160,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( ? [X3] : vplus(X1,X3) = X0
| ~ less(X1,X0) ) ),
inference(rectify,[],[f159]) ).
fof(f159,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( ? [X2] : vplus(X1,X2) = X0
| ~ less(X1,X0) ) ),
inference(nnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( less(X1,X0)
<=> ? [X2] : vplus(X1,X2) = X0 ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X77,X78] :
( less(X78,X77)
<=> ? [X79] : vplus(X78,X79) = X77 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof(f468,plain,
spl4_38,
inference(avatar_split_clause,[],[f195,f466]) ).
fof(f466,plain,
( spl4_38
<=> ! [X2,X0,X1] :
( vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_38])]) ).
fof(f195,plain,
! [X2,X0,X1] :
( vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1] :
( ! [X2] : vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( X0 != X1
=> ! [X2] : vplus(X2,X0) != vplus(X2,X1) ),
inference(rectify,[],[f49]) ).
fof(f49,axiom,
! [X87,X88] :
( X87 != X88
=> ! [X89] : vplus(X89,X87) != vplus(X89,X88) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
fof(f457,plain,
( spl4_37
| ~ spl4_3
| ~ spl4_19 ),
inference(avatar_split_clause,[],[f350,f333,f268,f454]) ).
fof(f454,plain,
( spl4_37
<=> less(vd512,vd511) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_37])]) ).
fof(f333,plain,
( spl4_19
<=> ! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_19])]) ).
fof(f350,plain,
( less(vd512,vd511)
| ~ spl4_3
| ~ spl4_19 ),
inference(resolution,[],[f334,f270]) ).
fof(f334,plain,
( ! [X0,X1] :
( ~ greater(X0,X1)
| less(X1,X0) )
| ~ spl4_19 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f442,plain,
spl4_36,
inference(avatar_split_clause,[],[f238,f440]) ).
fof(f440,plain,
( spl4_36
<=> ! [X0] :
( vplus(v1,vskolem2(X0)) = X0
| v1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_36])]) ).
fof(f238,plain,
! [X0] :
( vplus(v1,vskolem2(X0)) = X0
| v1 = X0 ),
inference(definition_unfolding,[],[f175,f174]) ).
fof(f174,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(rectify,[],[f53]) ).
fof(f53,axiom,
! [X96] : vplus(v1,X96) = vsucc(X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof(f175,plain,
! [X0] :
( vsucc(vskolem2(X0)) = X0
| v1 = X0 ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0] :
( vsucc(vskolem2(X0)) = X0
| v1 = X0 ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( v1 != X0
=> vsucc(vskolem2(X0)) = X0 ),
inference(rectify,[],[f56]) ).
fof(f56,axiom,
! [X102] :
( v1 != X102
=> vsucc(vskolem2(X102)) = X102 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
fof(f438,plain,
spl4_35,
inference(avatar_split_clause,[],[f231,f436]) ).
fof(f436,plain,
( spl4_35
<=> ! [X2,X0,X1] :
( less(X0,X2)
| ~ less(X0,X1)
| ~ leq(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_35])]) ).
fof(f231,plain,
! [X2,X0,X1] :
( less(X0,X2)
| ~ less(X0,X1)
| ~ leq(X1,X2) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0,X1,X2] :
( less(X0,X2)
| ( ( ~ less(X0,X1)
| ~ leq(X1,X2) )
& ( ~ leq(X0,X1)
| ~ less(X1,X2) ) ) ),
inference(ennf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ( ( less(X0,X1)
& leq(X1,X2) )
| ( leq(X0,X1)
& less(X1,X2) ) )
=> less(X0,X2) ),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X57,X58,X59] :
( ( ( less(X57,X58)
& leq(X58,X59) )
| ( leq(X57,X58)
& less(X58,X59) ) )
=> less(X57,X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(177), 0), 0)') ).
fof(f434,plain,
spl4_34,
inference(avatar_split_clause,[],[f230,f432]) ).
fof(f432,plain,
( spl4_34
<=> ! [X2,X0,X1] :
( less(X0,X2)
| ~ leq(X0,X1)
| ~ less(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_34])]) ).
fof(f230,plain,
! [X2,X0,X1] :
( less(X0,X2)
| ~ leq(X0,X1)
| ~ less(X1,X2) ),
inference(cnf_transformation,[],[f146]) ).
fof(f430,plain,
spl4_33,
inference(avatar_split_clause,[],[f229,f428]) ).
fof(f428,plain,
( spl4_33
<=> ! [X2,X0,X1] :
( less(X0,X2)
| ~ less(X0,X1)
| ~ less(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_33])]) ).
fof(f229,plain,
! [X2,X0,X1] :
( less(X0,X2)
| ~ less(X0,X1)
| ~ less(X1,X2) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0,X1,X2] :
( less(X0,X2)
| ~ less(X0,X1)
| ~ less(X1,X2) ),
inference(flattening,[],[f144]) ).
fof(f144,plain,
! [X0,X1,X2] :
( less(X0,X2)
| ~ less(X0,X1)
| ~ less(X1,X2) ),
inference(ennf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ( less(X0,X1)
& less(X1,X2) )
=> less(X0,X2) ),
inference(rectify,[],[f32]) ).
fof(f32,axiom,
! [X60,X61,X62] :
( ( less(X60,X61)
& less(X61,X62) )
=> less(X60,X62) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).
fof(f426,plain,
spl4_32,
inference(avatar_split_clause,[],[f228,f424]) ).
fof(f424,plain,
( spl4_32
<=> ! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_32])]) ).
fof(f228,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(flattening,[],[f142]) ).
fof(f142,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X0,X1)
| ~ leq(X1,X2) ),
inference(ennf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ( leq(X0,X1)
& leq(X1,X2) )
=> leq(X0,X2) ),
inference(rectify,[],[f30]) ).
fof(f30,axiom,
! [X54,X55,X56] :
( ( leq(X54,X55)
& leq(X55,X56) )
=> leq(X54,X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(184, 0), 0)') ).
fof(f422,plain,
( spl4_31
| ~ spl4_2
| ~ spl4_19 ),
inference(avatar_split_clause,[],[f349,f333,f263,f419]) ).
fof(f419,plain,
( spl4_31
<=> less(vd509,vd508) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_31])]) ).
fof(f349,plain,
( less(vd509,vd508)
| ~ spl4_2
| ~ spl4_19 ),
inference(resolution,[],[f334,f265]) ).
fof(f417,plain,
spl4_30,
inference(avatar_split_clause,[],[f206,f415]) ).
fof(f415,plain,
( spl4_30
<=> ! [X0,X1] :
( X0 = X1
| greater(X1,X0)
| ~ geq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_30])]) ).
fof(f206,plain,
! [X0,X1] :
( X0 = X1
| greater(X1,X0)
| ~ geq(X1,X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0,X1] :
( ( geq(X1,X0)
| ( X0 != X1
& ~ greater(X1,X0) ) )
& ( X0 = X1
| greater(X1,X0)
| ~ geq(X1,X0) ) ),
inference(flattening,[],[f157]) ).
fof(f157,plain,
! [X0,X1] :
( ( geq(X1,X0)
| ( X0 != X1
& ~ greater(X1,X0) ) )
& ( X0 = X1
| greater(X1,X0)
| ~ geq(X1,X0) ) ),
inference(nnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( geq(X1,X0)
<=> ( X0 = X1
| greater(X1,X0) ) ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X69,X70] :
( geq(X70,X69)
<=> ( X69 = X70
| greater(X70,X69) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
fof(f413,plain,
spl4_29,
inference(avatar_split_clause,[],[f203,f411]) ).
fof(f411,plain,
( spl4_29
<=> ! [X0,X1] :
( X0 = X1
| less(X1,X0)
| ~ leq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_29])]) ).
fof(f203,plain,
! [X0,X1] :
( X0 = X1
| less(X1,X0)
| ~ leq(X1,X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0,X1] :
( ( leq(X1,X0)
| ( X0 != X1
& ~ less(X1,X0) ) )
& ( X0 = X1
| less(X1,X0)
| ~ leq(X1,X0) ) ),
inference(flattening,[],[f155]) ).
fof(f155,plain,
! [X0,X1] :
( ( leq(X1,X0)
| ( X0 != X1
& ~ less(X1,X0) ) )
& ( X0 = X1
| less(X1,X0)
| ~ leq(X1,X0) ) ),
inference(nnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( leq(X1,X0)
<=> ( X0 = X1
| less(X1,X0) ) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X67,X68] :
( leq(X68,X67)
<=> ( X67 = X68
| less(X68,X67) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).
fof(f409,plain,
spl4_28,
inference(avatar_split_clause,[],[f191,f407]) ).
fof(f407,plain,
( spl4_28
<=> ! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_28])]) ).
fof(f191,plain,
! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
! [X75,X76] :
( less(X75,X76)
| greater(X75,X76)
| X75 = X76 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof(f399,plain,
spl4_27,
inference(avatar_split_clause,[],[f202,f397]) ).
fof(f397,plain,
( spl4_27
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ less(X0,vplus(X1,v1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_27])]) ).
fof(f202,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ less(X0,vplus(X1,v1)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ less(X0,vplus(X1,v1)) ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( less(X0,vplus(X1,v1))
=> leq(X0,X1) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X29,X30] :
( less(X29,vplus(X30,v1))
=> leq(X29,X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(241, 0), 0)') ).
fof(f395,plain,
spl4_26,
inference(avatar_split_clause,[],[f200,f393]) ).
fof(f393,plain,
( spl4_26
<=> ! [X0,X1] :
( geq(X0,vplus(X1,v1))
| ~ greater(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_26])]) ).
fof(f200,plain,
! [X0,X1] :
( geq(X0,vplus(X1,v1))
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0,X1] :
( geq(X0,vplus(X1,v1))
| ~ greater(X0,X1) ),
inference(ennf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( greater(X0,X1)
=> geq(X0,vplus(X1,v1)) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X31,X32] :
( greater(X31,X32)
=> geq(X31,vplus(X32,v1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(234, 0), 0)') ).
fof(f371,plain,
( spl4_25
| ~ spl4_4
| ~ spl4_17 ),
inference(avatar_split_clause,[],[f346,f325,f273,f369]) ).
fof(f369,plain,
( spl4_25
<=> ! [X0] : leq(v1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_25])]) ).
fof(f273,plain,
( spl4_4
<=> ! [X0] : geq(X0,v1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
fof(f325,plain,
( spl4_17
<=> ! [X0,X1] :
( leq(X1,X0)
| ~ geq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_17])]) ).
fof(f346,plain,
( ! [X0] : leq(v1,X0)
| ~ spl4_4
| ~ spl4_17 ),
inference(resolution,[],[f326,f274]) ).
fof(f274,plain,
( ! [X0] : geq(X0,v1)
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f326,plain,
( ! [X0,X1] :
( ~ geq(X0,X1)
| leq(X1,X0) )
| ~ spl4_17 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f367,plain,
spl4_24,
inference(avatar_split_clause,[],[f250,f365]) ).
fof(f365,plain,
( spl4_24
<=> ! [X2,X0,X3] : vplus(vplus(X0,X2),X3) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_24])]) ).
fof(f250,plain,
! [X2,X3,X0] : vplus(vplus(X0,X2),X3) != X0,
inference(equality_resolution,[],[f193]) ).
fof(f193,plain,
! [X2,X3,X0,X1] :
( vplus(X0,X2) != X1
| vplus(X1,X3) != X0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1] :
( ! [X2] : vplus(X0,X2) != X1
| ! [X3] : vplus(X1,X3) != X0 ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X0,X2) = X1
| ~ ? [X3] : vplus(X1,X3) = X0 ),
inference(rectify,[],[f47]) ).
fof(f47,axiom,
! [X83,X84] :
( ~ ? [X86] : vplus(X83,X86) = X84
| ~ ? [X85] : vplus(X84,X85) = X83 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
fof(f363,plain,
spl4_23,
inference(avatar_split_clause,[],[f179,f361]) ).
fof(f361,plain,
( spl4_23
<=> ! [X0,X1] : vplus(X0,X1) = vplus(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_23])]) ).
fof(f179,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(rectify,[],[f51]) ).
fof(f51,axiom,
! [X92,X93] : vplus(X93,X92) = vplus(X92,X93),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f359,plain,
spl4_22,
inference(avatar_split_clause,[],[f178,f357]) ).
fof(f357,plain,
( spl4_22
<=> ! [X0,X1] : vmul(X0,X1) = vmul(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_22])]) ).
fof(f178,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X22,X23] : vmul(X22,X23) = vmul(X23,X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof(f343,plain,
spl4_21,
inference(avatar_split_clause,[],[f207,f341]) ).
fof(f207,plain,
! [X0,X1] :
( geq(X1,X0)
| ~ greater(X1,X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f339,plain,
spl4_20,
inference(avatar_split_clause,[],[f204,f337]) ).
fof(f337,plain,
( spl4_20
<=> ! [X0,X1] :
( leq(X1,X0)
| ~ less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_20])]) ).
fof(f204,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ less(X1,X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f335,plain,
spl4_19,
inference(avatar_split_clause,[],[f199,f333]) ).
fof(f199,plain,
! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(ennf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( greater(X0,X1)
=> less(X1,X0) ),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X73,X74] :
( greater(X73,X74)
=> less(X74,X73) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof(f331,plain,
spl4_18,
inference(avatar_split_clause,[],[f198,f329]) ).
fof(f329,plain,
( spl4_18
<=> ! [X0,X1] :
( greater(X1,X0)
| ~ less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_18])]) ).
fof(f198,plain,
! [X0,X1] :
( greater(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0,X1] :
( greater(X1,X0)
| ~ less(X0,X1) ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( less(X0,X1)
=> greater(X1,X0) ),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X71,X72] :
( less(X71,X72)
=> greater(X72,X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof(f327,plain,
spl4_17,
inference(avatar_split_clause,[],[f197,f325]) ).
fof(f197,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ geq(X0,X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ geq(X0,X1) ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( geq(X0,X1)
=> leq(X1,X0) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X65,X66] :
( geq(X65,X66)
=> leq(X66,X65) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
fof(f323,plain,
spl4_16,
inference(avatar_split_clause,[],[f196,f321]) ).
fof(f321,plain,
( spl4_16
<=> ! [X0,X1] :
( geq(X1,X0)
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_16])]) ).
fof(f196,plain,
! [X0,X1] :
( geq(X1,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0,X1] :
( geq(X1,X0)
| ~ leq(X0,X1) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( leq(X0,X1)
=> geq(X1,X0) ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X63,X64] :
( leq(X63,X64)
=> geq(X64,X63) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
fof(f319,plain,
spl4_15,
inference(avatar_split_clause,[],[f190,f317]) ).
fof(f317,plain,
( spl4_15
<=> ! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_15])]) ).
fof(f190,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X75,X76] :
( ~ less(X75,X76)
| ~ greater(X75,X76) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof(f315,plain,
spl4_14,
inference(avatar_split_clause,[],[f253,f313]) ).
fof(f313,plain,
( spl4_14
<=> ! [X2,X1] : less(X1,vplus(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).
fof(f253,plain,
! [X2,X1] : less(X1,vplus(X1,X2)),
inference(equality_resolution,[],[f210]) ).
fof(f210,plain,
! [X2,X0,X1] :
( less(X1,X0)
| vplus(X1,X2) != X0 ),
inference(cnf_transformation,[],[f162]) ).
fof(f311,plain,
spl4_13,
inference(avatar_split_clause,[],[f248,f309]) ).
fof(f309,plain,
( spl4_13
<=> ! [X2,X0] : vplus(X0,X2) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).
fof(f248,plain,
! [X2,X0] : vplus(X0,X2) != X0,
inference(equality_resolution,[],[f188]) ).
fof(f188,plain,
! [X2,X0,X1] :
( vplus(X0,X2) != X1
| X0 != X1 ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0,X1] :
( ! [X2] : vplus(X0,X2) != X1
| X0 != X1 ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X0,X2) = X1
| X0 != X1 ),
inference(rectify,[],[f46]) ).
fof(f46,axiom,
! [X83,X84] :
( ~ ? [X86] : vplus(X83,X86) = X84
| X83 != X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof(f307,plain,
spl4_12,
inference(avatar_split_clause,[],[f185,f305]) ).
fof(f305,plain,
( spl4_12
<=> ! [X0] : vmul(X0,v1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).
fof(f185,plain,
! [X0] : vmul(X0,v1) = X0,
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( vmul(X0,v1) = X0
& vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X27,X28] :
( vmul(X27,v1) = X27
& vmul(X27,vsucc(X28)) = vplus(vmul(X27,X28),X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
fof(f303,plain,
spl4_11,
inference(avatar_split_clause,[],[f177,f301]) ).
fof(f301,plain,
( spl4_11
<=> ! [X0,X1] : greater(vplus(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).
fof(f177,plain,
! [X0,X1] : greater(vplus(X0,X1),X0),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] : greater(vplus(X0,X1),X0),
inference(rectify,[],[f29]) ).
fof(f29,axiom,
! [X52,X53] : greater(vplus(X52,X53),X52),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
fof(f299,plain,
spl4_10,
inference(avatar_split_clause,[],[f176,f297]) ).
fof(f297,plain,
( spl4_10
<=> ! [X0,X1] : vplus(X0,X1) != X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
fof(f176,plain,
! [X0,X1] : vplus(X0,X1) != X1,
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] : vplus(X0,X1) != X1,
inference(rectify,[],[f50]) ).
fof(f50,axiom,
! [X90,X91] : vplus(X90,X91) != X91,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof(f295,plain,
spl4_9,
inference(avatar_split_clause,[],[f173,f293]) ).
fof(f293,plain,
( spl4_9
<=> ! [X0] : vmul(v1,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
fof(f173,plain,
! [X0] : vmul(v1,X0) = X0,
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] : vmul(v1,X0) = X0,
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X26] : vmul(v1,X26) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
fof(f291,plain,
spl4_8,
inference(avatar_split_clause,[],[f252,f289]) ).
fof(f289,plain,
( spl4_8
<=> ! [X1] : geq(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
fof(f252,plain,
! [X1] : geq(X1,X1),
inference(equality_resolution,[],[f208]) ).
fof(f208,plain,
! [X0,X1] :
( geq(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f158]) ).
fof(f287,plain,
spl4_7,
inference(avatar_split_clause,[],[f251,f285]) ).
fof(f285,plain,
( spl4_7
<=> ! [X1] : leq(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
fof(f251,plain,
! [X1] : leq(X1,X1),
inference(equality_resolution,[],[f205]) ).
fof(f205,plain,
! [X0,X1] :
( leq(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f156]) ).
fof(f283,plain,
spl4_6,
inference(avatar_split_clause,[],[f247,f281]) ).
fof(f281,plain,
( spl4_6
<=> ! [X1] : ~ greater(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
fof(f247,plain,
! [X1] : ~ greater(X1,X1),
inference(equality_resolution,[],[f187]) ).
fof(f187,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| X0 != X1 ),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X75,X76] :
( ~ greater(X75,X76)
| X75 != X76 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
fof(f279,plain,
spl4_5,
inference(avatar_split_clause,[],[f246,f277]) ).
fof(f277,plain,
( spl4_5
<=> ! [X1] : ~ less(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
fof(f246,plain,
! [X1] : ~ less(X1,X1),
inference(equality_resolution,[],[f186]) ).
fof(f186,plain,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
inference(rectify,[],[f40]) ).
fof(f40,axiom,
! [X75,X76] :
( ~ less(X75,X76)
| X75 != X76 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
fof(f275,plain,
spl4_4,
inference(avatar_split_clause,[],[f170,f273]) ).
fof(f170,plain,
! [X0] : geq(X0,v1),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] : geq(X0,v1),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X33] : geq(X33,v1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(228, 0), 0)') ).
fof(f271,plain,
spl4_3,
inference(avatar_split_clause,[],[f169,f268]) ).
fof(f169,plain,
greater(vd511,vd512),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
greater(vd511,vd512),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(314), 513, 0)') ).
fof(f266,plain,
spl4_2,
inference(avatar_split_clause,[],[f168,f263]) ).
fof(f168,plain,
greater(vd508,vd509),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
greater(vd508,vd509),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(314), 510, 0)') ).
fof(f261,plain,
~ spl4_1,
inference(avatar_split_clause,[],[f167,f258]) ).
fof(f167,plain,
~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(flattening,[],[f2]) ).
fof(f2,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(315), 514, 0)') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM854+1 : TPTP v8.1.2. Released v4.1.0.
% 0.04/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n024.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 : Mon Apr 29 23:49:21 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (1125)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (1129)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 % (1128)WARNING: value z3 for option sas not known
% 0.13/0.37 % (1127)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37 % (1126)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 TRYING [1]
% 0.13/0.37 % (1128)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)
% 0.13/0.37 % (1130)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)
% 0.13/0.37 % (1133)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)
% 0.13/0.37 % (1131)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)
% 0.13/0.37 TRYING [2]
% 0.20/0.37 TRYING [3]
% 0.20/0.38 % (1130)First to succeed.
% 0.20/0.38 TRYING [1]
% 0.20/0.38 % (1130)Refutation found. Thanks to Tanya!
% 0.20/0.38 % SZS status Theorem for theBenchmark
% 0.20/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.39 % (1130)------------------------------
% 0.20/0.39 % (1130)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.39 % (1130)Termination reason: Refutation
% 0.20/0.39
% 0.20/0.39 % (1130)Memory used [KB]: 1020
% 0.20/0.39 % (1130)Time elapsed: 0.017 s
% 0.20/0.39 % (1130)Instructions burned: 25 (million)
% 0.20/0.39 % (1130)------------------------------
% 0.20/0.39 % (1130)------------------------------
% 0.20/0.39 % (1125)Success in time 0.033 s
%------------------------------------------------------------------------------