TSTP Solution File: NUM691^1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM691^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n021.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 : Sun May 5 08:41:53 EDT 2024
% Result : Theorem 0.21s 0.38s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 26
% Syntax : Number of formulae : 116 ( 4 unt; 16 typ; 0 def)
% Number of atoms : 817 ( 139 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 299 ( 154 ~; 99 |; 5 &; 0 @)
% ( 4 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 22 ( 21 >; 1 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 10 con; 0-6 aty)
% Number of variables : 73 ( 0 ^ 67 !; 0 ?; 73 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
nat: $tType ).
thf(func_def_1,type,
x: nat ).
thf(func_def_2,type,
y: nat ).
thf(func_def_3,type,
z: nat ).
thf(func_def_4,type,
u: nat ).
thf(func_def_5,type,
more: nat > nat > $o ).
thf(func_def_7,type,
pl: nat > nat > nat ).
thf(func_def_11,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_12,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_13,type,
vAND: $o > $o > $o ).
thf(func_def_14,type,
vOR: $o > $o > $o ).
thf(func_def_15,type,
vIMP: $o > $o > $o ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(func_def_17,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f169,plain,
$false,
inference(avatar_sat_refutation,[],[f84,f99,f114,f116,f118,f123,f144,f146,f148,f162,f165,f168]) ).
thf(f168,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f167]) ).
thf(f167,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f166,f79]) ).
thf(f79,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) = $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f77]) ).
thf(f77,plain,
( spl0_1
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f166,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f157,f94]) ).
thf(f94,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) = $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f92,plain,
( spl0_3
<=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f157,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true ) ),
inference(trivial_inequality_removal,[],[f156]) ).
thf(f156,plain,
( ( $true != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true ) ),
inference(superposition,[],[f36,f41]) ).
thf(f41,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f33,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) )
| ( ( X0 != X1 )
& ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ) ),
inference(flattening,[],[f32]) ).
thf(f32,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) )
| ( ( X0 != X1 )
& ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ) ),
inference(ennf_transformation,[],[f26]) ).
thf(f26,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
=> ( X0 = X1 ) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) ) ) ),
inference(flattening,[],[f19]) ).
thf(f19,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
=> ( X0 = X1 ) )
=> ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f18,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1)
=> ( X0 = X1 ) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) ) ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
! [X1: nat,X2: nat,X3: nat,X4: nat] :
( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X1),X2)
=> ( X1 = X2 ) )
=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X3),X4)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X2),X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz22a) ).
thf(f36,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u)) != $true,
inference(cnf_transformation,[],[f28]) ).
thf(f28,plain,
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u) )
& ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u)) != $true ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f22,plain,
~ ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u)) != $true )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u) ) ),
inference(flattening,[],[f11]) ).
thf(f11,plain,
~ ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u)) != $true )
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,plain,
~ ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u))
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u) ) ),
inference(rectify,[],[f7]) ).
thf(f7,negated_conjecture,
~ ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u))
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u) ) ),
inference(negated_conjecture,[],[f6]) ).
thf(f6,conjecture,
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u))
=> ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz23) ).
thf(f165,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f164]) ).
thf(f164,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f163,f79]) ).
thf(f163,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f158,f94]) ).
thf(f158,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true ) ),
inference(trivial_inequality_removal,[],[f155]) ).
thf(f155,plain,
( ( $true = $false )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true ) ),
inference(superposition,[],[f150,f41]) ).
thf(f150,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u)) = $false,
inference(trivial_inequality_removal,[],[f149]) ).
thf(f149,plain,
( ( $true != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u)) = $false ) ),
inference(superposition,[],[f36,f9]) ).
thf(f9,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f162,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f161]) ).
thf(f161,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f160,f79]) ).
thf(f160,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f159,f94]) ).
thf(f159,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true ) ),
inference(trivial_inequality_removal,[],[f154]) ).
thf(f154,plain,
( ( $true = $false )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true ) ),
inference(superposition,[],[f41,f150]) ).
thf(f148,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f147]) ).
thf(f147,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(subsumption_resolution,[],[f140,f79]) ).
thf(f140,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f139]) ).
thf(f139,plain,
( ( $true != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
| ~ spl0_4 ),
inference(superposition,[],[f124,f47]) ).
thf(f47,plain,
! [X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ),
inference(equality_resolution,[],[f44]) ).
thf(f44,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
| ( X2 != X3 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f35,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
| ( ( X2 != X3 )
& ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ),
inference(flattening,[],[f34]) ).
thf(f34,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
| ( ( X2 != X3 )
& ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) ) ),
inference(ennf_transformation,[],[f27]) ).
thf(f27,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
=> ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) )
=> ( X2 = X3 ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) ) ) ),
inference(flattening,[],[f21]) ).
thf(f21,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1) )
=> ( ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) )
=> ( X2 = X3 ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f20,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X0),X1)
=> ( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3)
=> ( X2 = X3 ) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) ) ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
! [X1: nat,X2: nat,X3: nat,X4: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X1),X2)
=> ( ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X3),X4)
=> ( X3 = X4 ) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X2),X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz22b) ).
thf(f124,plain,
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),z)) )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f36,f98]) ).
thf(f98,plain,
( ( z = u )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f96]) ).
thf(f96,plain,
( spl0_4
<=> ( z = u ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f146,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f145]) ).
thf(f145,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(subsumption_resolution,[],[f141,f79]) ).
thf(f141,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f138]) ).
thf(f138,plain,
( ( $true = $false )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
| ~ spl0_4 ),
inference(superposition,[],[f133,f47]) ).
thf(f133,plain,
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),z)) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f132]) ).
thf(f132,plain,
( ( $true != $true )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),z)) )
| ~ spl0_4 ),
inference(superposition,[],[f124,f9]) ).
thf(f144,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f143]) ).
thf(f143,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(subsumption_resolution,[],[f142,f79]) ).
thf(f142,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f137]) ).
thf(f137,plain,
( ( $true = $false )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
| ~ spl0_4 ),
inference(superposition,[],[f47,f133]) ).
thf(f123,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f122]) ).
thf(f122,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f121,plain,
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f100,f98]) ).
thf(f100,plain,
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),u) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f37,f83]) ).
thf(f83,plain,
( ( x = y )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f81]) ).
thf(f81,plain,
( spl0_2
<=> ( x = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f37,plain,
vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,y),u),
inference(cnf_transformation,[],[f28]) ).
thf(f118,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f117]) ).
thf(f117,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f110,f94]) ).
thf(f110,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f109,plain,
( ( $true != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
| ~ spl0_2 ),
inference(superposition,[],[f101,f46]) ).
thf(f46,plain,
! [X2: nat,X3: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) ) ),
inference(equality_resolution,[],[f42]) ).
thf(f42,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,X1),X3)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,X2),X3) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f101,plain,
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),u)) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f36,f83]) ).
thf(f116,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f115]) ).
thf(f115,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f111,f94]) ).
thf(f111,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f108]) ).
thf(f108,plain,
( ( $true = $false )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
| ~ spl0_2 ),
inference(superposition,[],[f103,f46]) ).
thf(f103,plain,
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),u)) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f102]) ).
thf(f102,plain,
( ( $true != $true )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),z)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),pl,x),u)) )
| ~ spl0_2 ),
inference(superposition,[],[f101,f9]) ).
thf(f114,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f113]) ).
thf(f113,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f112,f94]) ).
thf(f112,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f107]) ).
thf(f107,plain,
( ( $true = $false )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
| ~ spl0_2 ),
inference(superposition,[],[f46,f103]) ).
thf(f99,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f39,f96,f92]) ).
thf(f39,plain,
( ( z = u )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) = $true ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f30,plain,
( ( z = u )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) = $true ) ),
inference(ennf_transformation,[],[f24]) ).
thf(f24,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
=> ( z = u ) ),
inference(flattening,[],[f15]) ).
thf(f15,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u) != $true )
=> ( z = u ) ),
inference(fool_elimination,[],[f14]) ).
thf(f14,plain,
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u)
=> ( z = u ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,z),u)
=> ( z = u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(f84,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f38,f81,f77]) ).
thf(f38,plain,
( ( x = y )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) = $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f29,plain,
( ( x = y )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) = $true ) ),
inference(ennf_transformation,[],[f23]) ).
thf(f23,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
=> ( x = y ) ),
inference(flattening,[],[f13]) ).
thf(f13,plain,
( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y) != $true )
=> ( x = y ) ),
inference(fool_elimination,[],[f12]) ).
thf(f12,plain,
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y)
=> ( x = y ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),more,x),y)
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM691^1 : TPTP v8.1.2. Released v3.7.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n021.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 : Fri May 3 14:33:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (7714)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (7717)WARNING: value z3 for option sas not known
% 0.21/0.37 % (7716)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37 % (7717)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)
% 0.21/0.37 % (7718)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.37 % (7715)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37 % (7719)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)
% 0.21/0.37 % (7720)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)
% 0.21/0.37 % (7721)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)
% 0.21/0.37 % (7721)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.37 % Exception at run slice level% Exception at run slice level
% 0.21/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.37
% 0.21/0.37 % Exception at run slice level
% 0.21/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.38 % (7717)First to succeed.
% 0.21/0.38 % (7717)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7714"
% 0.21/0.38 % (7717)Refutation found. Thanks to Tanya!
% 0.21/0.38 % SZS status Theorem for theBenchmark
% 0.21/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38 % (7717)------------------------------
% 0.21/0.38 % (7717)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.38 % (7717)Termination reason: Refutation
% 0.21/0.38
% 0.21/0.38 % (7717)Memory used [KB]: 794
% 0.21/0.38 % (7717)Time elapsed: 0.011 s
% 0.21/0.38 % (7717)Instructions burned: 15 (million)
% 0.21/0.38 % (7714)Success in time 0.013 s
%------------------------------------------------------------------------------