TSTP Solution File: SEU861^5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU861^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n015.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 May 21 04:06:54 EDT 2024
% Result : Theorem 0.21s 0.41s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 39
% Syntax : Number of formulae : 145 ( 4 unt; 20 typ; 0 def)
% Number of atoms : 1748 ( 379 equ; 0 cnn)
% Maximal formula atoms : 18 ( 13 avg)
% Number of connectives : 648 ( 245 ~; 262 |; 85 &; 0 @)
% ( 11 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 226 ( 225 >; 1 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 13 con; 0-6 aty)
% Number of variables : 246 ( 0 ^ 190 !; 50 ?; 246 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cB: a > $o ).
thf(func_def_2,type,
cC: a > $o ).
thf(func_def_6,type,
sP0: ( ( a > $o ) > $o ) > $o ).
thf(func_def_7,type,
sK1: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_8,type,
sK2: ( ( a > $o ) > $o ) > a ).
thf(func_def_9,type,
sK3: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_10,type,
sK4: ( a > $o ) > $o ).
thf(func_def_11,type,
sK5: ( a > $o ) > a > ( a > $o ) > a ).
thf(func_def_12,type,
sK6: ( a > $o ) > a ).
thf(func_def_13,type,
sK7: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_15,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_16,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_17,type,
vAND: $o > $o > $o ).
thf(func_def_18,type,
vOR: $o > $o > $o ).
thf(func_def_19,type,
vIMP: $o > $o > $o ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(func_def_21,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f614,plain,
$false,
inference(avatar_sat_refutation,[],[f113,f151,f223,f273,f348,f360,f428,f536,f560,f562,f607,f609,f611,f613]) ).
thf(f613,plain,
~ spl8_11,
inference(avatar_contradiction_clause,[],[f612]) ).
thf(f612,plain,
( $false
| ~ spl8_11 ),
inference(equality_resolution,[],[f535]) ).
thf(f535,plain,
( ! [X0: a] : ( vAPP(sTfun(sTfun(a,$o),$o),a,sK2,sK4) != X0 )
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f534]) ).
thf(f534,plain,
( spl8_11
<=> ! [X0: a] : ( vAPP(sTfun(sTfun(a,$o),$o),a,sK2,sK4) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
thf(f611,plain,
( ~ spl8_2
| ~ spl8_10 ),
inference(avatar_contradiction_clause,[],[f610]) ).
thf(f610,plain,
( $false
| ~ spl8_2
| ~ spl8_10 ),
inference(subsumption_resolution,[],[f593,f111]) ).
thf(f111,plain,
( ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f110]) ).
thf(f110,plain,
( spl8_2
<=> ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
thf(f593,plain,
( ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f592]) ).
thf(f592,plain,
( ( $true != $true )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ( vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,sK4) != vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,sK4) )
| ~ spl8_10 ),
inference(constrained_superposition,[],[f23,f532]) ).
thf(f532,plain,
( ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,sK4)) )
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f530]) ).
thf(f530,plain,
( spl8_10
<=> ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).
thf(f23,plain,
! [X0: ( a > $o ) > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,X0,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)) )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
! [X0: ( a > $o ) > $o] :
( ( ( $true != vAPP(sTfun(a,$o),$o,X0,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)) )
& ! [X4: a] :
( ( vAPP(sTfun(sTfun(a,$o),$o),a,sK2,X0) = X4 )
| ( $true = vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0),X4) )
| ( $true != vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0),X4) ) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0)) ) )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f12,f13]) ).
thf(f13,plain,
! [X0: ( a > $o ) > $o] :
( ? [X1: a > $o,X2: a,X3: a > $o] :
( ( vAPP(sTfun(a,$o),$o,X0,X3) != $true )
& ! [X4: a] :
( ( X2 = X4 )
| ( $true = vAPP(a,$o,X1,X4) )
| ( $true != vAPP(a,$o,X3,X4) ) )
& ( vAPP(sTfun(a,$o),$o,X0,X1) = $true ) )
=> ( ( $true != vAPP(sTfun(a,$o),$o,X0,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)) )
& ! [X4: a] :
( ( vAPP(sTfun(sTfun(a,$o),$o),a,sK2,X0) = X4 )
| ( $true = vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0),X4) )
| ( $true != vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0),X4) ) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
! [X0: ( a > $o ) > $o] :
( ? [X1: a > $o,X2: a,X3: a > $o] :
( ( vAPP(sTfun(a,$o),$o,X0,X3) != $true )
& ! [X4: a] :
( ( X2 = X4 )
| ( $true = vAPP(a,$o,X1,X4) )
| ( $true != vAPP(a,$o,X3,X4) ) )
& ( vAPP(sTfun(a,$o),$o,X0,X1) = $true ) )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) ) ),
inference(rectify,[],[f11]) ).
thf(f11,plain,
! [X1: ( a > $o ) > $o] :
( ? [X2: a > $o,X3: a,X4: a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,X1,X4) )
& ! [X5: a] :
( ( X3 = X5 )
| ( $true = vAPP(a,$o,X2,X5) )
| ( $true != vAPP(a,$o,X4,X5) ) )
& ( $true = vAPP(sTfun(a,$o),$o,X1,X2) ) )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
thf(f9,plain,
! [X1: ( a > $o ) > $o] :
( ? [X2: a > $o,X3: a,X4: a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,X1,X4) )
& ! [X5: a] :
( ( X3 = X5 )
| ( $true = vAPP(a,$o,X2,X5) )
| ( $true != vAPP(a,$o,X4,X5) ) )
& ( $true = vAPP(sTfun(a,$o),$o,X1,X2) ) )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f609,plain,
( ~ spl8_2
| ~ spl8_10 ),
inference(avatar_contradiction_clause,[],[f608]) ).
thf(f608,plain,
( $false
| ~ spl8_2
| ~ spl8_10 ),
inference(subsumption_resolution,[],[f594,f111]) ).
thf(f594,plain,
( ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f591]) ).
thf(f591,plain,
( ( $true = $false )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ( vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,sK4) != vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,sK4) )
| ~ spl8_10 ),
inference(constrained_superposition,[],[f122,f532]) ).
thf(f122,plain,
! [X0: ( a > $o ) > $o] :
( ( $false = vAPP(sTfun(a,$o),$o,X0,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)) )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) ) ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f121,plain,
! [X0: ( a > $o ) > $o] :
( ( $true != $true )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) )
| ( $false = vAPP(sTfun(a,$o),$o,X0,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)) ) ),
inference(superposition,[],[f23,f4]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f607,plain,
( ~ spl8_2
| ~ spl8_10 ),
inference(avatar_contradiction_clause,[],[f606]) ).
thf(f606,plain,
( $false
| ~ spl8_2
| ~ spl8_10 ),
inference(subsumption_resolution,[],[f602,f111]) ).
thf(f602,plain,
( ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f582]) ).
thf(f582,plain,
( ( $true = $false )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ( vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,sK4) != vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,sK4) )
| ~ spl8_10 ),
inference(constrained_superposition,[],[f532,f122]) ).
thf(f562,plain,
( ~ spl8_2
| ~ spl8_9 ),
inference(avatar_contradiction_clause,[],[f561]) ).
thf(f561,plain,
( $false
| ~ spl8_2
| ~ spl8_9 ),
inference(subsumption_resolution,[],[f550,f111]) ).
thf(f550,plain,
( ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ~ spl8_9 ),
inference(trivial_inequality_removal,[],[f548]) ).
thf(f548,plain,
( ( $true = $false )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ( vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,sK4) != vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,sK4) )
| ~ spl8_9 ),
inference(constrained_superposition,[],[f21,f528]) ).
thf(f528,plain,
( ( $false = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,sK4)) )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f526]) ).
thf(f526,plain,
( spl8_9
<=> ( $false = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).
thf(f21,plain,
! [X0: ( a > $o ) > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,X0,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0)) )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f560,plain,
( ~ spl8_2
| ~ spl8_9 ),
inference(avatar_contradiction_clause,[],[f559]) ).
thf(f559,plain,
( $false
| ~ spl8_2
| ~ spl8_9 ),
inference(subsumption_resolution,[],[f554,f111]) ).
thf(f554,plain,
( ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ~ spl8_9 ),
inference(trivial_inequality_removal,[],[f540]) ).
thf(f540,plain,
( ( $true = $false )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ( vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,sK4) != vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,sK4) )
| ~ spl8_9 ),
inference(constrained_superposition,[],[f528,f21]) ).
thf(f536,plain,
( spl8_9
| spl8_10
| spl8_11
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f524,f110,f534,f530,f526]) ).
thf(f524,plain,
( ! [X0: a] :
( ( vAPP(sTfun(sTfun(a,$o),$o),a,sK2,sK4) != X0 )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,sK4)) )
| ( $false = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,sK4)) ) )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[],[f520]) ).
thf(f520,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(sTfun(sTfun(a,$o),$o),a,sK2,sK4) != X0 )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,sK4)) )
| ( $false = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,sK4)) ) )
| ~ spl8_2 ),
inference(superposition,[],[f514,f111]) ).
thf(f514,plain,
! [X0: ( a > $o ) > $o,X1: a] :
( ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) )
| ( vAPP(sTfun(sTfun(a,$o),$o),a,sK2,X0) != X1 )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)) )
| ( $false = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0)) ) ),
inference(trivial_inequality_removal,[],[f513]) ).
thf(f513,plain,
! [X0: ( a > $o ) > $o,X1: a] :
( ( $true != $true )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)) )
| ( vAPP(sTfun(sTfun(a,$o),$o),a,sK2,X0) != X1 )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) )
| ( $false = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0)) ) ),
inference(superposition,[],[f499,f4]) ).
thf(f499,plain,
! [X0: ( a > $o ) > $o,X1: a] :
( ( $true != vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0)) )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)) )
| ( vAPP(sTfun(sTfun(a,$o),$o),a,sK2,X0) != X1 )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) ) ),
inference(duplicate_literal_removal,[],[f492]) ).
thf(f492,plain,
! [X0: ( a > $o ) > $o,X1: a] :
( ( vAPP(sTfun(sTfun(a,$o),$o),a,sK2,X0) != X1 )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0)) )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)) )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) ) ),
inference(superposition,[],[f30,f479]) ).
thf(f479,plain,
! [X0: ( a > $o ) > $o,X1: a] :
( ( vAPP(sTfun(sTfun(a,$o),$o),a,sK2,X0) = vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)),X1),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0)) )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)) )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) ) ),
inference(trivial_inequality_removal,[],[f478]) ).
thf(f478,plain,
! [X0: ( a > $o ) > $o,X1: a] :
( ( $true != $true )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0)) )
| ( vAPP(sTfun(sTfun(a,$o),$o),a,sK2,X0) = vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)),X1),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0)) )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) ) ),
inference(duplicate_literal_removal,[],[f477]) ).
thf(f477,plain,
! [X0: ( a > $o ) > $o,X1: a] :
( ( $true != $true )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0)) )
| ( vAPP(sTfun(sTfun(a,$o),$o),a,sK2,X0) = vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)),X1),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0)) )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0)) ) ),
inference(superposition,[],[f29,f308]) ).
thf(f308,plain,
! [X2: a > $o,X0: ( a > $o ) > $o,X1: a] :
( ( $true = vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0),vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)),X1),X2)) )
| ( vAPP(sTfun(sTfun(a,$o),$o),a,sK2,X0) = vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)),X1),X2) )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,X2) ) ),
inference(trivial_inequality_removal,[],[f305]) ).
thf(f305,plain,
! [X2: a > $o,X0: ( a > $o ) > $o,X1: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0),vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)),X1),X2)) )
| ( vAPP(sTfun(sTfun(a,$o),$o),a,sK2,X0) = vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)),X1),X2) )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,X2) ) ),
inference(superposition,[],[f22,f28]) ).
thf(f28,plain,
! [X2: a,X3: a > $o,X1: a > $o] :
( ( $true = vAPP(a,$o,X3,vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,X3),X2),X1)) )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,X3) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,X1) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f20,plain,
( ( $true != vAPP(sTfun(a,$o),$o,sK4,cB) )
& ! [X1: a > $o,X2: a,X3: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,sK4,X3) )
| ( ( vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,X3),X2),X1) != X2 )
& ( $true != vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,X3),X2),X1)) )
& ( $true = vAPP(a,$o,X3,vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,X3),X2),X1)) ) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,X1) ) )
& ! [X5: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,sK4,X5) )
| ( $true = vAPP(a,$o,X5,vAPP(sTfun(a,$o),a,sK6,X5)) ) )
& ! [X7: a] :
( ( $true = vAPP(a,$o,cC,X7) )
| ( $true != vAPP(a,$o,cB,X7) ) )
& ! [X8: ( a > $o ) > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,X8,cC) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X8) )
| ( ( $true != vAPP(sTfun(a,$o),$o,X8,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,X8)) )
& ! [X10: a] : ( $true != vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,X8),X10) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f15,f19,f18,f17,f16]) ).
thf(f16,plain,
( ? [X0: ( a > $o ) > $o] :
( ( vAPP(sTfun(a,$o),$o,X0,cB) != $true )
& ! [X1: a > $o,X2: a,X3: a > $o] :
( ( vAPP(sTfun(a,$o),$o,X0,X3) = $true )
| ? [X4: a] :
( ( X2 != X4 )
& ( $true != vAPP(a,$o,X1,X4) )
& ( $true = vAPP(a,$o,X3,X4) ) )
| ( vAPP(sTfun(a,$o),$o,X0,X1) != $true ) )
& ! [X5: a > $o] :
( ( vAPP(sTfun(a,$o),$o,X0,X5) = $true )
| ? [X6: a] : ( vAPP(a,$o,X5,X6) = $true ) ) )
=> ( ( $true != vAPP(sTfun(a,$o),$o,sK4,cB) )
& ! [X3: a > $o,X2: a,X1: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,sK4,X3) )
| ? [X4: a] :
( ( X2 != X4 )
& ( $true != vAPP(a,$o,X1,X4) )
& ( $true = vAPP(a,$o,X3,X4) ) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,X1) ) )
& ! [X5: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,sK4,X5) )
| ? [X6: a] : ( vAPP(a,$o,X5,X6) = $true ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f17,plain,
! [X1: a > $o,X2: a,X3: a > $o] :
( ? [X4: a] :
( ( X2 != X4 )
& ( $true != vAPP(a,$o,X1,X4) )
& ( $true = vAPP(a,$o,X3,X4) ) )
=> ( ( vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,X3),X2),X1) != X2 )
& ( $true != vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,X3),X2),X1)) )
& ( $true = vAPP(a,$o,X3,vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,X3),X2),X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f18,plain,
! [X5: a > $o] :
( ? [X6: a] : ( vAPP(a,$o,X5,X6) = $true )
=> ( $true = vAPP(a,$o,X5,vAPP(sTfun(a,$o),a,sK6,X5)) ) ),
introduced(choice_axiom,[]) ).
thf(f19,plain,
! [X8: ( a > $o ) > $o] :
( ? [X9: a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,X8,X9) )
& ! [X10: a] : ( $true != vAPP(a,$o,X9,X10) ) )
=> ( ( $true != vAPP(sTfun(a,$o),$o,X8,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,X8)) )
& ! [X10: a] : ( $true != vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,X8),X10) ) ) ),
introduced(choice_axiom,[]) ).
thf(f15,plain,
( ? [X0: ( a > $o ) > $o] :
( ( vAPP(sTfun(a,$o),$o,X0,cB) != $true )
& ! [X1: a > $o,X2: a,X3: a > $o] :
( ( vAPP(sTfun(a,$o),$o,X0,X3) = $true )
| ? [X4: a] :
( ( X2 != X4 )
& ( $true != vAPP(a,$o,X1,X4) )
& ( $true = vAPP(a,$o,X3,X4) ) )
| ( vAPP(sTfun(a,$o),$o,X0,X1) != $true ) )
& ! [X5: a > $o] :
( ( vAPP(sTfun(a,$o),$o,X0,X5) = $true )
| ? [X6: a] : ( vAPP(a,$o,X5,X6) = $true ) ) )
& ! [X7: a] :
( ( $true = vAPP(a,$o,cC,X7) )
| ( $true != vAPP(a,$o,cB,X7) ) )
& ! [X8: ( a > $o ) > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,X8,cC) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X8) )
| ? [X9: a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,X8,X9) )
& ! [X10: a] : ( $true != vAPP(a,$o,X9,X10) ) ) ) ),
inference(rectify,[],[f10]) ).
thf(f10,plain,
( ? [X8: ( a > $o ) > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,X8,cB) )
& ! [X9: a > $o,X10: a,X11: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,X8,X11) )
| ? [X12: a] :
( ( X10 != X12 )
& ( $true != vAPP(a,$o,X9,X12) )
& ( $true = vAPP(a,$o,X11,X12) ) )
| ( $true != vAPP(sTfun(a,$o),$o,X8,X9) ) )
& ! [X13: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,X8,X13) )
| ? [X14: a] : ( $true = vAPP(a,$o,X13,X14) ) ) )
& ! [X0: a] :
( ( $true = vAPP(a,$o,cC,X0) )
| ( $true != vAPP(a,$o,cB,X0) ) )
& ! [X1: ( a > $o ) > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,X1,cC) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X1) )
| ? [X6: a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,X1,X6) )
& ! [X7: a] : ( $true != vAPP(a,$o,X6,X7) ) ) ) ),
inference(definition_folding,[],[f8,f9]) ).
thf(f8,plain,
( ? [X8: ( a > $o ) > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,X8,cB) )
& ! [X9: a > $o,X10: a,X11: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,X8,X11) )
| ? [X12: a] :
( ( X10 != X12 )
& ( $true != vAPP(a,$o,X9,X12) )
& ( $true = vAPP(a,$o,X11,X12) ) )
| ( $true != vAPP(sTfun(a,$o),$o,X8,X9) ) )
& ! [X13: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,X8,X13) )
| ? [X14: a] : ( $true = vAPP(a,$o,X13,X14) ) ) )
& ! [X0: a] :
( ( $true = vAPP(a,$o,cC,X0) )
| ( $true != vAPP(a,$o,cB,X0) ) )
& ! [X1: ( a > $o ) > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,X1,cC) )
| ? [X2: a > $o,X3: a,X4: a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,X1,X4) )
& ! [X5: a] :
( ( X3 = X5 )
| ( $true = vAPP(a,$o,X2,X5) )
| ( $true != vAPP(a,$o,X4,X5) ) )
& ( $true = vAPP(sTfun(a,$o),$o,X1,X2) ) )
| ? [X6: a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,X1,X6) )
& ! [X7: a] : ( $true != vAPP(a,$o,X6,X7) ) ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
( ? [X8: ( a > $o ) > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,X8,cB) )
& ! [X9: a > $o,X10: a,X11: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,X8,X11) )
| ? [X12: a] :
( ( X10 != X12 )
& ( $true != vAPP(a,$o,X9,X12) )
& ( $true = vAPP(a,$o,X11,X12) ) )
| ( $true != vAPP(sTfun(a,$o),$o,X8,X9) ) )
& ! [X13: a > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,X8,X13) )
| ? [X14: a] : ( $true = vAPP(a,$o,X13,X14) ) ) )
& ! [X0: a] :
( ( $true = vAPP(a,$o,cC,X0) )
| ( $true != vAPP(a,$o,cB,X0) ) )
& ! [X1: ( a > $o ) > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,X1,cC) )
| ? [X2: a > $o,X3: a,X4: a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,X1,X4) )
& ! [X5: a] :
( ( X3 = X5 )
| ( $true = vAPP(a,$o,X2,X5) )
| ( $true != vAPP(a,$o,X4,X5) ) )
& ( $true = vAPP(sTfun(a,$o),$o,X1,X2) ) )
| ? [X6: a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,X1,X6) )
& ! [X7: a] : ( $true != vAPP(a,$o,X6,X7) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ( ( ! [X0: a] :
( ( $true = vAPP(a,$o,cB,X0) )
=> ( $true = vAPP(a,$o,cC,X0) ) )
& ! [X1: ( a > $o ) > $o] :
( ( ! [X2: a > $o,X3: a,X4: a > $o] :
( ( ! [X5: a] :
( ( $true = vAPP(a,$o,X4,X5) )
=> ( ( X3 = X5 )
| ( $true = vAPP(a,$o,X2,X5) ) ) )
& ( $true = vAPP(sTfun(a,$o),$o,X1,X2) ) )
=> ( $true = vAPP(sTfun(a,$o),$o,X1,X4) ) )
& ! [X6: a > $o] :
( ~ ? [X7: a] : ( $true = vAPP(a,$o,X6,X7) )
=> ( $true = vAPP(sTfun(a,$o),$o,X1,X6) ) ) )
=> ( $true = vAPP(sTfun(a,$o),$o,X1,cC) ) ) )
=> ! [X8: ( a > $o ) > $o] :
( ( ! [X9: a > $o,X10: a,X11: a > $o] :
( ( ! [X12: a] :
( ( $true = vAPP(a,$o,X11,X12) )
=> ( ( X10 = X12 )
| ( $true = vAPP(a,$o,X9,X12) ) ) )
& ( $true = vAPP(sTfun(a,$o),$o,X8,X9) ) )
=> ( $true = vAPP(sTfun(a,$o),$o,X8,X11) ) )
& ! [X13: a > $o] :
( ~ ? [X14: a] : ( $true = vAPP(a,$o,X13,X14) )
=> ( $true = vAPP(sTfun(a,$o),$o,X8,X13) ) ) )
=> ( $true = vAPP(sTfun(a,$o),$o,X8,cB) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: a] :
( vAPP(a,$o,cB,X0)
=> vAPP(a,$o,cC,X0) )
& ! [X1: ( a > $o ) > $o] :
( ( ! [X2: a > $o,X3: a,X4: a > $o] :
( ( ! [X5: a] :
( vAPP(a,$o,X4,X5)
=> ( ( X3 = X5 )
| vAPP(a,$o,X2,X5) ) )
& vAPP(sTfun(a,$o),$o,X1,X2) )
=> vAPP(sTfun(a,$o),$o,X1,X4) )
& ! [X6: a > $o] :
( ~ ? [X7: a] : vAPP(a,$o,X6,X7)
=> vAPP(sTfun(a,$o),$o,X1,X6) ) )
=> vAPP(sTfun(a,$o),$o,X1,cC) ) )
=> ! [X8: ( a > $o ) > $o] :
( ( ! [X9: a > $o,X10: a,X11: a > $o] :
( ( ! [X12: a] :
( vAPP(a,$o,X11,X12)
=> ( ( X10 = X12 )
| vAPP(a,$o,X9,X12) ) )
& vAPP(sTfun(a,$o),$o,X8,X9) )
=> vAPP(sTfun(a,$o),$o,X8,X11) )
& ! [X13: a > $o] :
( ~ ? [X14: a] : vAPP(a,$o,X13,X14)
=> vAPP(sTfun(a,$o),$o,X8,X13) ) )
=> vAPP(sTfun(a,$o),$o,X8,cB) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X4: a] :
( vAPP(a,$o,cB,X4)
=> vAPP(a,$o,cC,X4) )
& ! [X0: ( a > $o ) > $o] :
( ( ! [X3: a > $o,X4: a,X5: a > $o] :
( ( ! [X6: a] :
( vAPP(a,$o,X5,X6)
=> ( ( X4 = X6 )
| vAPP(a,$o,X3,X6) ) )
& vAPP(sTfun(a,$o),$o,X0,X3) )
=> vAPP(sTfun(a,$o),$o,X0,X5) )
& ! [X1: a > $o] :
( ~ ? [X2: a] : vAPP(a,$o,X1,X2)
=> vAPP(sTfun(a,$o),$o,X0,X1) ) )
=> vAPP(sTfun(a,$o),$o,X0,cC) ) )
=> ! [X0: ( a > $o ) > $o] :
( ( ! [X3: a > $o,X4: a,X5: a > $o] :
( ( ! [X7: a] :
( vAPP(a,$o,X5,X7)
=> ( ( X4 = X7 )
| vAPP(a,$o,X3,X7) ) )
& vAPP(sTfun(a,$o),$o,X0,X3) )
=> vAPP(sTfun(a,$o),$o,X0,X5) )
& ! [X1: a > $o] :
( ~ ? [X2: a] : vAPP(a,$o,X1,X2)
=> vAPP(sTfun(a,$o),$o,X0,X1) ) )
=> vAPP(sTfun(a,$o),$o,X0,cB) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ( ! [X4: a] :
( vAPP(a,$o,cB,X4)
=> vAPP(a,$o,cC,X4) )
& ! [X0: ( a > $o ) > $o] :
( ( ! [X3: a > $o,X4: a,X5: a > $o] :
( ( ! [X6: a] :
( vAPP(a,$o,X5,X6)
=> ( ( X4 = X6 )
| vAPP(a,$o,X3,X6) ) )
& vAPP(sTfun(a,$o),$o,X0,X3) )
=> vAPP(sTfun(a,$o),$o,X0,X5) )
& ! [X1: a > $o] :
( ~ ? [X2: a] : vAPP(a,$o,X1,X2)
=> vAPP(sTfun(a,$o),$o,X0,X1) ) )
=> vAPP(sTfun(a,$o),$o,X0,cC) ) )
=> ! [X0: ( a > $o ) > $o] :
( ( ! [X3: a > $o,X4: a,X5: a > $o] :
( ( ! [X7: a] :
( vAPP(a,$o,X5,X7)
=> ( ( X4 = X7 )
| vAPP(a,$o,X3,X7) ) )
& vAPP(sTfun(a,$o),$o,X0,X3) )
=> vAPP(sTfun(a,$o),$o,X0,X5) )
& ! [X1: a > $o] :
( ~ ? [X2: a] : vAPP(a,$o,X1,X2)
=> vAPP(sTfun(a,$o),$o,X0,X1) ) )
=> vAPP(sTfun(a,$o),$o,X0,cB) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM531E_pme) ).
thf(f22,plain,
! [X0: ( a > $o ) > $o,X4: a] :
( ( $true != vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK3,X0),X4) )
| ( $true = vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,X0),X4) )
| ( vAPP(sTfun(sTfun(a,$o),$o),a,sK2,X0) = X4 )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f29,plain,
! [X2: a,X3: a > $o,X1: a > $o] :
( ( $true != vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,X3),X2),X1)) )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,X3) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,X1) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f30,plain,
! [X2: a,X3: a > $o,X1: a > $o] :
( ( vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,X3),X2),X1) != X2 )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,X3) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,X1) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f428,plain,
( spl8_7
| spl8_8 ),
inference(avatar_split_clause,[],[f85,f425,f421]) ).
thf(f421,plain,
( spl8_7
<=> ( cC = vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,vAPP(sTfun(sTfun(a,$o),$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun($o,$o),sTfun(sTfun(sTfun(a,$o),$o),sTfun(sTfun(a,$o),$o)),bCOMB,vNOT),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vEQ(sTfun(a,$o)),cC))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
thf(f425,plain,
( spl8_8
<=> ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,vAPP(sTfun(sTfun(a,$o),$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun($o,$o),sTfun(sTfun(sTfun(a,$o),$o),sTfun(sTfun(a,$o),$o)),bCOMB,vNOT),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vEQ(sTfun(a,$o)),cC))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
thf(f85,plain,
( ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,vAPP(sTfun(sTfun(a,$o),$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun($o,$o),sTfun(sTfun(sTfun(a,$o),$o),sTfun(sTfun(a,$o),$o)),bCOMB,vNOT),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vEQ(sTfun(a,$o)),cC))) )
| ( cC = vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,vAPP(sTfun(sTfun(a,$o),$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun($o,$o),sTfun(sTfun(sTfun(a,$o),$o),sTfun(sTfun(a,$o),$o)),bCOMB,vNOT),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vEQ(sTfun(a,$o)),cC))) ) ),
inference(leibniz_equality_elimination,[],[f25]) ).
thf(f25,plain,
! [X8: ( a > $o ) > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,X8,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,X8)) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X8) )
| ( $true = vAPP(sTfun(a,$o),$o,X8,cC) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f360,plain,
( ~ spl8_2
| ~ spl8_5 ),
inference(avatar_contradiction_clause,[],[f359]) ).
thf(f359,plain,
( $false
| ~ spl8_2
| ~ spl8_5 ),
inference(subsumption_resolution,[],[f357,f111]) ).
thf(f357,plain,
( ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f352]) ).
thf(f352,plain,
( ( $true != $true )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ~ spl8_5 ),
inference(superposition,[],[f344,f21]) ).
thf(f344,plain,
( ! [X2: a > $o] : ( $true != vAPP(sTfun(a,$o),$o,sK4,X2) )
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f343]) ).
thf(f343,plain,
( spl8_5
<=> ! [X2: a > $o] : ( $true != vAPP(sTfun(a,$o),$o,sK4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
thf(f348,plain,
( spl8_5
| spl8_6 ),
inference(avatar_split_clause,[],[f336,f346,f343]) ).
thf(f346,plain,
( spl8_6
<=> ! [X0: a,X1: a] :
( ( X0 != X1 )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(a,sTfun(a,$o),vEQ(a),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
thf(f336,plain,
! [X2: a > $o,X0: a,X1: a] :
( ( X0 != X1 )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(a,sTfun(a,$o),vEQ(a),X0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,X2) ) ),
inference(duplicate_literal_removal,[],[f335]) ).
thf(f335,plain,
! [X2: a > $o,X0: a,X1: a] :
( ( X0 != X1 )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(a,sTfun(a,$o),vEQ(a),X0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,X2) )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(a,sTfun(a,$o),vEQ(a),X0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,X2) ) ),
inference(superposition,[],[f30,f253]) ).
thf(f253,plain,
! [X2: a > $o,X0: a,X1: a] :
( ( vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,vAPP(a,sTfun(a,$o),vEQ(a),X0)),X1),X2) = X0 )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(a,sTfun(a,$o),vEQ(a),X0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,X2) ) ),
inference(equality_proxy_clausification,[],[f246]) ).
thf(f246,plain,
! [X2: a > $o,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,vAPP(a,sTfun(a,$o),vEQ(a),X0)),X1),X2)) )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(a,sTfun(a,$o),vEQ(a),X0)) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,X2) ) ),
inference(primitive_instantiation,[],[f28]) ).
thf(f273,plain,
~ spl8_4,
inference(avatar_contradiction_clause,[],[f272]) ).
thf(f272,plain,
( $false
| ~ spl8_4 ),
inference(subsumption_resolution,[],[f271,f150]) ).
thf(f150,plain,
( ( $true = vAPP(sTfun(a,$o),$o,sK4,cC) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f148]) ).
thf(f148,plain,
( spl8_4
<=> ( $true = vAPP(sTfun(a,$o),$o,sK4,cC) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
thf(f271,plain,
( ( $true != vAPP(sTfun(a,$o),$o,sK4,cC) )
| ~ spl8_4 ),
inference(subsumption_resolution,[],[f270,f31]) ).
thf(f31,plain,
$true != vAPP(sTfun(a,$o),$o,sK4,cB),
inference(cnf_transformation,[],[f20]) ).
thf(f270,plain,
( ( $true = vAPP(sTfun(a,$o),$o,sK4,cB) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,cC) )
| ~ spl8_4 ),
inference(trivial_inequality_removal,[],[f269]) ).
thf(f269,plain,
( ( $true != $true )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,cB) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,cC) )
| ~ spl8_4 ),
inference(duplicate_literal_removal,[],[f266]) ).
thf(f266,plain,
( ( $true != $true )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,cB) )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,cB) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,cC) )
| ~ spl8_4 ),
inference(superposition,[],[f265,f28]) ).
thf(f265,plain,
( ! [X0: a > $o,X1: a] :
( ( $true != vAPP(a,$o,cB,vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,X0),X1),cC)) )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,X0) ) )
| ~ spl8_4 ),
inference(subsumption_resolution,[],[f263,f150]) ).
thf(f263,plain,
! [X0: a > $o,X1: a] :
( ( $true = vAPP(sTfun(a,$o),$o,sK4,X0) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,cC) )
| ( $true != vAPP(a,$o,cB,vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,X0),X1),cC)) ) ),
inference(trivial_inequality_removal,[],[f257]) ).
thf(f257,plain,
! [X0: a > $o,X1: a] :
( ( $true != $true )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,X0) )
| ( $true != vAPP(sTfun(a,$o),$o,sK4,cC) )
| ( $true != vAPP(a,$o,cB,vAPP(sTfun(a,$o),a,vAPP(a,sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(a,sTfun(sTfun(a,$o),a)),sK5,X0),X1),cC)) ) ),
inference(superposition,[],[f29,f26]) ).
thf(f26,plain,
! [X7: a] :
( ( $true = vAPP(a,$o,cC,X7) )
| ( $true != vAPP(a,$o,cB,X7) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f223,plain,
( spl8_2
| spl8_4 ),
inference(avatar_contradiction_clause,[],[f222]) ).
thf(f222,plain,
( $false
| spl8_2
| spl8_4 ),
inference(subsumption_resolution,[],[f221,f149]) ).
thf(f149,plain,
( ( $true != vAPP(sTfun(a,$o),$o,sK4,cC) )
| spl8_4 ),
inference(avatar_component_clause,[],[f148]) ).
thf(f221,plain,
( ( $true = vAPP(sTfun(a,$o),$o,sK4,cC) )
| spl8_2
| spl8_4 ),
inference(subsumption_resolution,[],[f220,f112]) ).
thf(f112,plain,
( ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| spl8_2 ),
inference(avatar_component_clause,[],[f110]) ).
thf(f220,plain,
( ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,cC) )
| spl8_2
| spl8_4 ),
inference(equality_resolution,[],[f195]) ).
thf(f195,plain,
( ! [X0: ( a > $o ) > $o] :
( ( vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,X0) != vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,sK4) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) )
| ( vAPP(sTfun(a,$o),$o,X0,cC) = $true ) )
| spl8_2
| spl8_4 ),
inference(subsumption_resolution,[],[f194,f112]) ).
thf(f194,plain,
( ! [X0: ( a > $o ) > $o] :
( ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ( vAPP(sTfun(a,$o),$o,X0,cC) = $true )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) )
| ( vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,X0) != vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,sK4) ) )
| spl8_4 ),
inference(subsumption_resolution,[],[f191,f149]) ).
thf(f191,plain,
! [X0: ( a > $o ) > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,sK4,cC) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ( vAPP(sTfun(a,$o),$o,X0,cC) = $true )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) )
| ( vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,X0) != vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,sK4) ) ),
inference(trivial_inequality_removal,[],[f177]) ).
thf(f177,plain,
! [X0: ( a > $o ) > $o] :
( ( $true = $false )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,cC) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ( vAPP(sTfun(a,$o),$o,X0,cC) = $true )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) )
| ( vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,X0) != vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,sK4) ) ),
inference(constrained_superposition,[],[f91,f76]) ).
thf(f76,plain,
! [X0: ( a > $o ) > $o] :
( ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,X0)) )
| ( vAPP(sTfun(a,$o),$o,X0,cC) = $true )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) ) ),
inference(trivial_inequality_removal,[],[f73]) ).
thf(f73,plain,
! [X0: ( a > $o ) > $o] :
( ( $true != $true )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) )
| ( vAPP(sTfun(a,$o),$o,X0,cC) = $true )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,X0)) ) ),
inference(superposition,[],[f24,f27]) ).
thf(f27,plain,
! [X5: a > $o] :
( ( $true = vAPP(a,$o,X5,vAPP(sTfun(a,$o),a,sK6,X5)) )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,X5) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f24,plain,
! [X10: a,X8: ( a > $o ) > $o] :
( ( $true != vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,X8),X10) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X8) )
| ( $true = vAPP(sTfun(a,$o),$o,X8,cC) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f91,plain,
! [X0: ( a > $o ) > $o] :
( ( $false = vAPP(sTfun(a,$o),$o,X0,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,X0)) )
| ( vAPP(sTfun(a,$o),$o,X0,cC) = $true )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) ) ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f90,plain,
! [X0: ( a > $o ) > $o] :
( ( $true != $true )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,X0) )
| ( vAPP(sTfun(a,$o),$o,X0,cC) = $true )
| ( $false = vAPP(sTfun(a,$o),$o,X0,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,X0)) ) ),
inference(superposition,[],[f25,f4]) ).
thf(f151,plain,
( ~ spl8_3
| spl8_4
| spl8_2 ),
inference(avatar_split_clause,[],[f142,f110,f148,f144]) ).
thf(f144,plain,
( spl8_3
<=> ( cC = vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
thf(f142,plain,
( ( $true = vAPP(sTfun(a,$o),$o,sK4,cC) )
| ( cC != vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,sK4) )
| spl8_2 ),
inference(subsumption_resolution,[],[f135,f112]) ).
thf(f135,plain,
( ( $true = vAPP(sTfun(a,$o),$o,sK4,cC) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ( cC != vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,sK4) ) ),
inference(trivial_inequality_removal,[],[f134]) ).
thf(f134,plain,
( ( $true != $true )
| ( $true = vAPP(sTfun(a,$o),$o,sK4,cC) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ( cC != vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK7,sK4) ) ),
inference(equality_factoring,[],[f76]) ).
thf(f113,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f101,f110,f106]) ).
thf(f106,plain,
( spl8_1
<=> ( cB = vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
thf(f101,plain,
( ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ( cB != vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,sK4) ) ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f99,plain,
( ( $true != $true )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP0,sK4) )
| ( cB != vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK1,sK4) ) ),
inference(constrained_superposition,[],[f31,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU861^5 : TPTP v8.2.0. Released v4.0.0.
% 0.15/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 19 17:12:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (5728)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (5733)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 % (5731)WARNING: value z3 for option sas not known
% 0.21/0.38 % (5729)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (5730)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 % (5731)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)
% 0.21/0.38 % (5732)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 % (5734)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)
% 0.21/0.38 % (5735)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)
% 0.21/0.38 % Exception at run slice level
% 0.21/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.38 % Exception at run slice level
% 0.21/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.38 % Exception at run slice level
% 0.21/0.38 % (5735)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.39 % (5736)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.39 % (5737)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.21/0.39 % (5738)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.21/0.39 % (5736)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.39 % (5737)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.40 % Exception at run slice level
% 0.21/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.40 % (5731)First to succeed.
% 0.21/0.41 % (5731)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-5728"
% 0.21/0.41 % (5731)Refutation found. Thanks to Tanya!
% 0.21/0.41 % SZS status Theorem for theBenchmark
% 0.21/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.41 % (5731)------------------------------
% 0.21/0.41 % (5731)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.41 % (5731)Termination reason: Refutation
% 0.21/0.41
% 0.21/0.41 % (5731)Memory used [KB]: 1009
% 0.21/0.41 % (5731)Time elapsed: 0.032 s
% 0.21/0.41 % (5731)Instructions burned: 54 (million)
% 0.21/0.41 % (5728)Success in time 0.047 s
%------------------------------------------------------------------------------