TSTP Solution File: NUM837+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM837+2 : 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 : n010.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 14:37:48 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 63
% Syntax : Number of formulae : 201 ( 46 unt; 0 def)
% Number of atoms : 458 ( 142 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 444 ( 187 ~; 182 |; 14 &)
% ( 47 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 45 ( 43 usr; 40 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 298 ( 274 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f366,plain,
$false,
inference(avatar_sat_refutation,[],[f109,f114,f119,f123,f127,f131,f135,f139,f143,f147,f151,f155,f159,f163,f167,f171,f175,f191,f195,f199,f203,f207,f216,f220,f225,f229,f239,f253,f280,f285,f301,f305,f311,f315,f319,f328,f347,f352,f365]) ).
fof(f365,plain,
( ~ spl4_1
| ~ spl4_38 ),
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f364,plain,
( $false
| ~ spl4_1
| ~ spl4_38 ),
inference(trivial_inequality_removal,[],[f353]) ).
fof(f353,plain,
( vd269 != vd269
| ~ spl4_1
| ~ spl4_38 ),
inference(superposition,[],[f108,f346]) ).
fof(f346,plain,
( vd269 = vplus(vd268,sK3(vd269,vd268))
| ~ spl4_38 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f344,plain,
( spl4_38
<=> vd269 = vplus(vd268,sK3(vd269,vd268)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_38])]) ).
fof(f108,plain,
( ! [X0] : vd269 != vplus(vd268,X0)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f107,plain,
( spl4_1
<=> ! [X0] : vd269 != vplus(vd268,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f352,plain,
( spl4_39
| ~ spl4_3
| ~ spl4_26 ),
inference(avatar_split_clause,[],[f233,f227,f116,f349]) ).
fof(f349,plain,
( spl4_39
<=> vd271 = vplus(vd269,sK3(vd271,vd269)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_39])]) ).
fof(f116,plain,
( spl4_3
<=> less(vd269,vd271) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
fof(f227,plain,
( spl4_26
<=> ! [X0,X1] :
( vplus(X1,sK3(X0,X1)) = X0
| ~ less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_26])]) ).
fof(f233,plain,
( vd271 = vplus(vd269,sK3(vd271,vd269))
| ~ spl4_3
| ~ spl4_26 ),
inference(resolution,[],[f228,f118]) ).
fof(f118,plain,
( less(vd269,vd271)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f228,plain,
( ! [X0,X1] :
( ~ less(X1,X0)
| vplus(X1,sK3(X0,X1)) = X0 )
| ~ spl4_26 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f347,plain,
( spl4_38
| ~ spl4_2
| ~ spl4_26 ),
inference(avatar_split_clause,[],[f232,f227,f111,f344]) ).
fof(f111,plain,
( spl4_2
<=> less(vd268,vd269) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f232,plain,
( vd269 = vplus(vd268,sK3(vd269,vd268))
| ~ spl4_2
| ~ spl4_26 ),
inference(resolution,[],[f228,f113]) ).
fof(f113,plain,
( less(vd268,vd269)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f328,plain,
( spl4_36
| spl4_37
| ~ spl4_31 ),
inference(avatar_split_clause,[],[f306,f299,f325,f321]) ).
fof(f321,plain,
( spl4_36
<=> vd269 = vd268 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_36])]) ).
fof(f325,plain,
( spl4_37
<=> vd268 = vplus(vd269,sK0(vd269,vd268)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_37])]) ).
fof(f299,plain,
( spl4_31
<=> ! [X0] :
( vd269 != X0
| vd268 = vplus(X0,sK0(X0,vd268))
| vd268 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_31])]) ).
fof(f306,plain,
( vd268 = vplus(vd269,sK0(vd269,vd268))
| vd269 = vd268
| ~ spl4_31 ),
inference(equality_resolution,[],[f300]) ).
fof(f300,plain,
( ! [X0] :
( vd269 != X0
| vd268 = vplus(X0,sK0(X0,vd268))
| vd268 = X0 )
| ~ spl4_31 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f319,plain,
( spl4_35
| ~ spl4_10
| ~ spl4_17 ),
inference(avatar_split_clause,[],[f186,f173,f145,f317]) ).
fof(f317,plain,
( spl4_35
<=> ! [X0,X1] : leq(X0,vplus(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_35])]) ).
fof(f145,plain,
( spl4_10
<=> ! [X2,X1] : less(X1,vplus(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
fof(f173,plain,
( spl4_17
<=> ! [X0,X1] :
( leq(X1,X0)
| ~ less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_17])]) ).
fof(f186,plain,
( ! [X0,X1] : leq(X0,vplus(X0,X1))
| ~ spl4_10
| ~ spl4_17 ),
inference(resolution,[],[f174,f146]) ).
fof(f146,plain,
( ! [X2,X1] : less(X1,vplus(X1,X2))
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f174,plain,
( ! [X0,X1] :
( ~ less(X1,X0)
| leq(X1,X0) )
| ~ spl4_17 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f315,plain,
( spl4_34
| ~ spl4_9
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f183,f169,f141,f313]) ).
fof(f313,plain,
( spl4_34
<=> ! [X0,X1] : geq(vplus(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_34])]) ).
fof(f141,plain,
( spl4_9
<=> ! [X2,X0] : greater(vplus(X0,X2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
fof(f169,plain,
( spl4_16
<=> ! [X0,X1] :
( geq(X1,X0)
| ~ greater(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_16])]) ).
fof(f183,plain,
( ! [X0,X1] : geq(vplus(X0,X1),X0)
| ~ spl4_9
| ~ spl4_16 ),
inference(resolution,[],[f170,f142]) ).
fof(f142,plain,
( ! [X2,X0] : greater(vplus(X0,X2),X0)
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f170,plain,
( ! [X0,X1] :
( ~ greater(X1,X0)
| geq(X1,X0) )
| ~ spl4_16 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f311,plain,
( spl4_33
| ~ spl4_9
| ~ spl4_11 ),
inference(avatar_split_clause,[],[f176,f149,f141,f309]) ).
fof(f309,plain,
( spl4_33
<=> ! [X0,X1] : ~ less(vplus(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_33])]) ).
fof(f149,plain,
( spl4_11
<=> ! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).
fof(f176,plain,
( ! [X0,X1] : ~ less(vplus(X0,X1),X0)
| ~ spl4_9
| ~ spl4_11 ),
inference(resolution,[],[f150,f142]) ).
fof(f150,plain,
( ! [X0,X1] :
( ~ greater(X0,X1)
| ~ less(X0,X1) )
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f305,plain,
( spl4_32
| ~ spl4_1
| ~ spl4_28 ),
inference(avatar_split_clause,[],[f266,f251,f107,f303]) ).
fof(f303,plain,
( spl4_32
<=> ! [X0] :
( vd269 != X0
| vd268 = vplus(X0,sK1(vd268,X0))
| vd268 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_32])]) ).
fof(f251,plain,
( spl4_28
<=> ! [X0,X1] :
( vplus(X0,sK0(X0,X1)) = X1
| vplus(X1,sK1(X0,X1)) = X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_28])]) ).
fof(f266,plain,
( ! [X0] :
( vd269 != X0
| vd268 = vplus(X0,sK1(vd268,X0))
| vd268 = X0 )
| ~ spl4_1
| ~ spl4_28 ),
inference(superposition,[],[f108,f252]) ).
fof(f252,plain,
( ! [X0,X1] :
( vplus(X1,sK1(X0,X1)) = X0
| vplus(X0,sK0(X0,X1)) = X1
| X0 = X1 )
| ~ spl4_28 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f301,plain,
( spl4_31
| ~ spl4_1
| ~ spl4_28 ),
inference(avatar_split_clause,[],[f256,f251,f107,f299]) ).
fof(f256,plain,
( ! [X0] :
( vd269 != X0
| vd268 = vplus(X0,sK0(X0,vd268))
| vd268 = X0 )
| ~ spl4_1
| ~ spl4_28 ),
inference(superposition,[],[f108,f252]) ).
fof(f285,plain,
( spl4_30
| ~ spl4_3
| ~ spl4_17 ),
inference(avatar_split_clause,[],[f185,f173,f116,f282]) ).
fof(f282,plain,
( spl4_30
<=> leq(vd269,vd271) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_30])]) ).
fof(f185,plain,
( leq(vd269,vd271)
| ~ spl4_3
| ~ spl4_17 ),
inference(resolution,[],[f174,f118]) ).
fof(f280,plain,
( spl4_29
| ~ spl4_2
| ~ spl4_17 ),
inference(avatar_split_clause,[],[f184,f173,f111,f277]) ).
fof(f277,plain,
( spl4_29
<=> leq(vd268,vd269) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_29])]) ).
fof(f184,plain,
( leq(vd268,vd269)
| ~ spl4_2
| ~ spl4_17 ),
inference(resolution,[],[f174,f113]) ).
fof(f253,plain,
spl4_28,
inference(avatar_split_clause,[],[f78,f251]) ).
fof(f78,plain,
! [X0,X1] :
( vplus(X0,sK0(X0,X1)) = X1
| vplus(X1,sK1(X0,X1)) = X0
| X0 = X1 ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( vplus(X0,sK0(X0,X1)) = X1
| vplus(X1,sK1(X0,X1)) = X0
| X0 = X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f31,f53,f52]) ).
fof(f52,plain,
! [X0,X1] :
( ? [X2] : vplus(X0,X2) = X1
=> vplus(X0,sK0(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
! [X0,X1] :
( ? [X3] : vplus(X1,X3) = X0
=> vplus(X1,sK1(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X1] :
( ? [X2] : vplus(X0,X2) = X1
| ? [X3] : vplus(X1,X3) = X0
| X0 = X1 ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X21,X22] :
( ? [X24] : vplus(X21,X24) = X22
| ? [X23] : vplus(X22,X23) = X21
| X21 = X22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
fof(f239,plain,
spl4_27,
inference(avatar_split_clause,[],[f95,f237]) ).
fof(f237,plain,
( spl4_27
<=> ! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_27])]) ).
fof(f95,plain,
! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X28,X29,X30] : vplus(vplus(X28,X29),X30) = vplus(X28,vplus(X29,X30)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof(f229,plain,
spl4_26,
inference(avatar_split_clause,[],[f93,f227]) ).
fof(f93,plain,
! [X0,X1] :
( vplus(X1,sK3(X0,X1)) = X0
| ~ less(X1,X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( vplus(X1,sK3(X0,X1)) = X0
| ~ less(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f64,f65]) ).
fof(f65,plain,
! [X0,X1] :
( ? [X3] : vplus(X1,X3) = X0
=> vplus(X1,sK3(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( ? [X3] : vplus(X1,X3) = X0
| ~ less(X1,X0) ) ),
inference(rectify,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( ? [X2] : vplus(X1,X2) = X0
| ~ less(X1,X0) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( less(X1,X0)
<=> ? [X2] : vplus(X1,X2) = X0 ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X15,X16] :
( less(X16,X15)
<=> ? [X17] : vplus(X16,X17) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof(f225,plain,
( spl4_25
| ~ spl4_3
| ~ spl4_15 ),
inference(avatar_split_clause,[],[f181,f165,f116,f222]) ).
fof(f222,plain,
( spl4_25
<=> greater(vd271,vd269) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_25])]) ).
fof(f165,plain,
( spl4_15
<=> ! [X0,X1] :
( greater(X1,X0)
| ~ less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_15])]) ).
fof(f181,plain,
( greater(vd271,vd269)
| ~ spl4_3
| ~ spl4_15 ),
inference(resolution,[],[f166,f118]) ).
fof(f166,plain,
( ! [X0,X1] :
( ~ less(X0,X1)
| greater(X1,X0) )
| ~ spl4_15 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f220,plain,
spl4_24,
inference(avatar_split_clause,[],[f91,f218]) ).
fof(f218,plain,
( spl4_24
<=> ! [X0,X1] :
( vplus(X0,sK2(X0,X1)) = X1
| ~ greater(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_24])]) ).
fof(f91,plain,
! [X0,X1] :
( vplus(X0,sK2(X0,X1)) = X1
| ~ greater(X1,X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( vplus(X0,sK2(X0,X1)) = X1
| ~ greater(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f60,f61]) ).
fof(f61,plain,
! [X0,X1] :
( ? [X3] : vplus(X0,X3) = X1
=> vplus(X0,sK2(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X3] : vplus(X0,X3) = X1
| ~ greater(X1,X0) ) ),
inference(rectify,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X2] : vplus(X0,X2) = X1
| ~ greater(X1,X0) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( greater(X1,X0)
<=> ? [X2] : vplus(X0,X2) = X1 ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X18,X19] :
( greater(X19,X18)
<=> ? [X20] : vplus(X18,X20) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof(f216,plain,
spl4_23,
inference(avatar_split_clause,[],[f80,f214]) ).
fof(f214,plain,
( spl4_23
<=> ! [X2,X0,X1] :
( vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_23])]) ).
fof(f80,plain,
! [X2,X0,X1] :
( vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( ! [X2] : vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( X0 != X1
=> ! [X2] : vplus(X2,X0) != vplus(X2,X1) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X25,X26] :
( X25 != X26
=> ! [X27] : vplus(X27,X25) != vplus(X27,X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
fof(f207,plain,
spl4_22,
inference(avatar_split_clause,[],[f88,f205]) ).
fof(f205,plain,
( spl4_22
<=> ! [X0,X1] :
( X0 = X1
| less(X1,X0)
| ~ leq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_22])]) ).
fof(f88,plain,
! [X0,X1] :
( X0 = X1
| less(X1,X0)
| ~ leq(X1,X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( ( leq(X1,X0)
| ( X0 != X1
& ~ less(X1,X0) ) )
& ( X0 = X1
| less(X1,X0)
| ~ leq(X1,X0) ) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( ( leq(X1,X0)
| ( X0 != X1
& ~ less(X1,X0) ) )
& ( X0 = X1
| less(X1,X0)
| ~ leq(X1,X0) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( leq(X1,X0)
<=> ( X0 = X1
| less(X1,X0) ) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X5,X6] :
( leq(X6,X5)
<=> ( X5 = X6
| less(X6,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).
fof(f203,plain,
spl4_21,
inference(avatar_split_clause,[],[f85,f201]) ).
fof(f201,plain,
( spl4_21
<=> ! [X0,X1] :
( X0 = X1
| greater(X1,X0)
| ~ geq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_21])]) ).
fof(f85,plain,
! [X0,X1] :
( X0 = X1
| greater(X1,X0)
| ~ geq(X1,X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( ( geq(X1,X0)
| ( X0 != X1
& ~ greater(X1,X0) ) )
& ( X0 = X1
| greater(X1,X0)
| ~ geq(X1,X0) ) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( ( geq(X1,X0)
| ( X0 != X1
& ~ greater(X1,X0) ) )
& ( X0 = X1
| greater(X1,X0)
| ~ geq(X1,X0) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( geq(X1,X0)
<=> ( X0 = X1
| greater(X1,X0) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X7,X8] :
( geq(X8,X7)
<=> ( X7 = X8
| greater(X8,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
fof(f199,plain,
spl4_20,
inference(avatar_split_clause,[],[f77,f197]) ).
fof(f197,plain,
( spl4_20
<=> ! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_20])]) ).
fof(f77,plain,
! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X13,X14] :
( less(X13,X14)
| greater(X13,X14)
| X13 = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof(f195,plain,
spl4_19,
inference(avatar_split_clause,[],[f101,f193]) ).
fof(f193,plain,
( spl4_19
<=> ! [X2,X0,X3] : vplus(vplus(X0,X2),X3) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_19])]) ).
fof(f101,plain,
! [X2,X3,X0] : vplus(vplus(X0,X2),X3) != X0,
inference(equality_resolution,[],[f79]) ).
fof(f79,plain,
! [X2,X3,X0,X1] :
( vplus(X0,X2) != X1
| vplus(X1,X3) != X0 ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( ! [X2] : vplus(X0,X2) != X1
| ! [X3] : vplus(X1,X3) != X0 ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X0,X2) = X1
| ~ ? [X3] : vplus(X1,X3) = X0 ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X21,X22] :
( ~ ? [X24] : vplus(X21,X24) = X22
| ~ ? [X23] : vplus(X22,X23) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
fof(f191,plain,
( spl4_18
| ~ spl4_2
| ~ spl4_15 ),
inference(avatar_split_clause,[],[f180,f165,f111,f188]) ).
fof(f188,plain,
( spl4_18
<=> greater(vd269,vd268) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_18])]) ).
fof(f180,plain,
( greater(vd269,vd268)
| ~ spl4_2
| ~ spl4_15 ),
inference(resolution,[],[f166,f113]) ).
fof(f175,plain,
spl4_17,
inference(avatar_split_clause,[],[f89,f173]) ).
fof(f89,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ less(X1,X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f171,plain,
spl4_16,
inference(avatar_split_clause,[],[f86,f169]) ).
fof(f86,plain,
! [X0,X1] :
( geq(X1,X0)
| ~ greater(X1,X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f167,plain,
spl4_15,
inference(avatar_split_clause,[],[f84,f165]) ).
fof(f84,plain,
! [X0,X1] :
( greater(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( greater(X1,X0)
| ~ less(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( less(X0,X1)
=> greater(X1,X0) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X9,X10] :
( less(X9,X10)
=> greater(X10,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof(f163,plain,
spl4_14,
inference(avatar_split_clause,[],[f83,f161]) ).
fof(f161,plain,
( spl4_14
<=> ! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).
fof(f83,plain,
! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( greater(X0,X1)
=> less(X1,X0) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X11,X12] :
( greater(X11,X12)
=> less(X12,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof(f159,plain,
spl4_13,
inference(avatar_split_clause,[],[f82,f157]) ).
fof(f157,plain,
( spl4_13
<=> ! [X0,X1] :
( leq(X1,X0)
| ~ geq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).
fof(f82,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ geq(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ geq(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( geq(X0,X1)
=> leq(X1,X0) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X3,X4] :
( geq(X3,X4)
=> leq(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
fof(f155,plain,
spl4_12,
inference(avatar_split_clause,[],[f81,f153]) ).
fof(f153,plain,
( spl4_12
<=> ! [X0,X1] :
( geq(X1,X0)
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).
fof(f81,plain,
! [X0,X1] :
( geq(X1,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( geq(X1,X0)
| ~ leq(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( leq(X0,X1)
=> geq(X1,X0) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X2] :
( leq(X1,X2)
=> geq(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
fof(f151,plain,
spl4_11,
inference(avatar_split_clause,[],[f76,f149]) ).
fof(f76,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X13,X14] :
( ~ less(X13,X14)
| ~ greater(X13,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof(f147,plain,
spl4_10,
inference(avatar_split_clause,[],[f105,f145]) ).
fof(f105,plain,
! [X2,X1] : less(X1,vplus(X1,X2)),
inference(equality_resolution,[],[f94]) ).
fof(f94,plain,
! [X2,X0,X1] :
( less(X1,X0)
| vplus(X1,X2) != X0 ),
inference(cnf_transformation,[],[f66]) ).
fof(f143,plain,
spl4_9,
inference(avatar_split_clause,[],[f104,f141]) ).
fof(f104,plain,
! [X2,X0] : greater(vplus(X0,X2),X0),
inference(equality_resolution,[],[f92]) ).
fof(f92,plain,
! [X2,X0,X1] :
( greater(X1,X0)
| vplus(X0,X2) != X1 ),
inference(cnf_transformation,[],[f62]) ).
fof(f139,plain,
spl4_8,
inference(avatar_split_clause,[],[f99,f137]) ).
fof(f137,plain,
( spl4_8
<=> ! [X2,X0] : vplus(X0,X2) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
fof(f99,plain,
! [X2,X0] : vplus(X0,X2) != X0,
inference(equality_resolution,[],[f74]) ).
fof(f74,plain,
! [X2,X0,X1] :
( vplus(X0,X2) != X1
| X0 != X1 ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( ! [X2] : vplus(X0,X2) != X1
| X0 != X1 ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X0,X2) = X1
| X0 != X1 ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X21,X22] :
( ~ ? [X24] : vplus(X21,X24) = X22
| X21 != X22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof(f135,plain,
spl4_7,
inference(avatar_split_clause,[],[f103,f133]) ).
fof(f133,plain,
( spl4_7
<=> ! [X1] : leq(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
fof(f103,plain,
! [X1] : leq(X1,X1),
inference(equality_resolution,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( leq(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f58]) ).
fof(f131,plain,
spl4_6,
inference(avatar_split_clause,[],[f102,f129]) ).
fof(f129,plain,
( spl4_6
<=> ! [X1] : geq(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
fof(f102,plain,
! [X1] : geq(X1,X1),
inference(equality_resolution,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( geq(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f56]) ).
fof(f127,plain,
spl4_5,
inference(avatar_split_clause,[],[f98,f125]) ).
fof(f125,plain,
( spl4_5
<=> ! [X1] : ~ less(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
fof(f98,plain,
! [X1] : ~ less(X1,X1),
inference(equality_resolution,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X13,X14] :
( ~ less(X13,X14)
| X13 != X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
fof(f123,plain,
spl4_4,
inference(avatar_split_clause,[],[f97,f121]) ).
fof(f121,plain,
( spl4_4
<=> ! [X1] : ~ greater(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
fof(f97,plain,
! [X1] : ~ greater(X1,X1),
inference(equality_resolution,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| X0 != X1 ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X13,X14] :
( ~ greater(X13,X14)
| X13 != X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
fof(f119,plain,
spl4_3,
inference(avatar_split_clause,[],[f69,f116]) ).
fof(f69,plain,
less(vd269,vd271),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
less(vd269,vd271),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','(conjunct2(170),272,0)') ).
fof(f114,plain,
spl4_2,
inference(avatar_split_clause,[],[f68,f111]) ).
fof(f68,plain,
less(vd268,vd269),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
less(vd268,vd269),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(170), 270, 0)') ).
fof(f109,plain,
spl4_1,
inference(avatar_split_clause,[],[f67,f107]) ).
fof(f67,plain,
! [X0] : vd269 != vplus(vd268,X0),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] : vd269 != vplus(vd268,X0),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ? [X0] : vd269 = vplus(vd268,X0),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
? [X0] : vd269 = vplus(vd268,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qe(171)') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM837+2 : TPTP v8.1.2. Released v4.1.0.
% 0.10/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 23:25:20 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (11872)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (11876)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (11875)WARNING: value z3 for option sas not known
% 0.14/0.37 TRYING [1]
% 0.14/0.37 % (11873)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 TRYING [2]
% 0.14/0.37 % (11875)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)
% 0.14/0.37 % (11874)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (11877)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)
% 0.14/0.37 % (11878)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)
% 0.14/0.37 % (11879)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)
% 0.14/0.37 TRYING [3]
% 0.14/0.37 TRYING [4]
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 % (11877)First to succeed.
% 0.14/0.38 TRYING [4]
% 0.14/0.38 % (11875)Also succeeded, but the first one will report.
% 0.14/0.38 % (11877)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38 % (11877)------------------------------
% 0.14/0.38 % (11877)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (11877)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (11877)Memory used [KB]: 917
% 0.14/0.38 % (11877)Time elapsed: 0.011 s
% 0.14/0.38 % (11877)Instructions burned: 15 (million)
% 0.14/0.38 % (11877)------------------------------
% 0.14/0.38 % (11877)------------------------------
% 0.14/0.38 % (11872)Success in time 0.028 s
%------------------------------------------------------------------------------