TSTP Solution File: SEV009^5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEV009^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n007.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 09:43:37 EDT 2024
% Result : Theorem 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 48
% Syntax : Number of formulae : 164 ( 5 unt; 24 typ; 0 def)
% Number of atoms : 2096 ( 447 equ; 0 cnn)
% Maximal formula atoms : 28 ( 14 avg)
% Number of connectives : 809 ( 298 ~; 301 |; 175 &; 0 @)
% ( 11 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 245 ( 244 >; 1 *; 0 +; 0 <<)
% Number of symbols : 37 ( 34 usr; 17 con; 0-6 aty)
% Number of variables : 277 ( 0 ^ 171 !; 100 ?; 277 :)
% ( 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_4,type,
sP0: ( ( a > $o ) > $o ) > a > a > $o ).
thf(func_def_5,type,
sP1: ( ( a > $o ) > $o ) > a > a > $o ).
thf(func_def_6,type,
sP2: ( ( a > $o ) > $o ) > $o ).
thf(func_def_7,type,
sK3: ( ( a > $o ) > $o ) > a ).
thf(func_def_8,type,
sK4: ( ( a > $o ) > $o ) > a ).
thf(func_def_9,type,
sK5: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_10,type,
sK6: ( ( a > $o ) > $o ) > a > a > a > $o ).
thf(func_def_11,type,
sK7: ( ( a > $o ) > $o ) > a > a > a > $o ).
thf(func_def_12,type,
sK8: ( a > $o ) > $o ).
thf(func_def_13,type,
sK9: a ).
thf(func_def_14,type,
sK10: a ).
thf(func_def_15,type,
sK11: a ).
thf(func_def_16,type,
sK12: a ).
thf(func_def_17,type,
sK13: a > a > $o ).
thf(func_def_19,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_20,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_21,type,
vAND: $o > $o > $o ).
thf(func_def_22,type,
vOR: $o > $o > $o ).
thf(func_def_23,type,
vIMP: $o > $o > $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f916,plain,
$false,
inference(avatar_sat_refutation,[],[f61,f66,f71,f186,f324,f602,f720,f745,f797,f845,f856,f915]) ).
thf(f915,plain,
( ~ spl14_4
| ~ spl14_5
| ~ spl14_18
| spl14_19
| ~ spl14_23
| ~ spl14_25 ),
inference(avatar_contradiction_clause,[],[f914]) ).
thf(f914,plain,
( $false
| ~ spl14_4
| ~ spl14_5
| ~ spl14_18
| spl14_19
| ~ spl14_23
| ~ spl14_25 ),
inference(trivial_inequality_removal,[],[f913]) ).
thf(f913,plain,
( ( $true = $false )
| ~ spl14_4
| ~ spl14_5
| ~ spl14_18
| spl14_19
| ~ spl14_23
| ~ spl14_25 ),
inference(forward_demodulation,[],[f909,f319]) ).
thf(f319,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK13,sK9),sK11) )
| ~ spl14_18 ),
inference(avatar_component_clause,[],[f317]) ).
thf(f317,plain,
( spl14_18
<=> ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK13,sK9),sK11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_18])]) ).
thf(f909,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK13,sK9),sK11) )
| ~ spl14_4
| ~ spl14_5
| spl14_19
| ~ spl14_23
| ~ spl14_25 ),
inference(backward_demodulation,[],[f800,f905]) ).
thf(f905,plain,
( ( vAPP(a,sTfun(a,$o),sK13,sK9) = vAPP(a,sTfun(a,$o),sK13,sK10) )
| ~ spl14_5
| spl14_19
| ~ spl14_25 ),
inference(subsumption_resolution,[],[f904,f322]) ).
thf(f322,plain,
( ( $false != vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),sK13,sK9)) )
| spl14_19 ),
inference(avatar_component_clause,[],[f321]) ).
thf(f321,plain,
( spl14_19
<=> ( $false = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),sK13,sK9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_19])]) ).
thf(f904,plain,
( ( vAPP(a,sTfun(a,$o),sK13,sK9) = vAPP(a,sTfun(a,$o),sK13,sK10) )
| ( $false = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),sK13,sK9)) )
| ~ spl14_5
| ~ spl14_25 ),
inference(trivial_inequality_removal,[],[f897]) ).
thf(f897,plain,
( ( $true = $false )
| ( vAPP(a,sTfun(a,$o),sK13,sK9) = vAPP(a,sTfun(a,$o),sK13,sK10) )
| ( $false = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),sK13,sK9)) )
| ~ spl14_5
| ~ spl14_25 ),
inference(superposition,[],[f854,f109]) ).
thf(f109,plain,
! [X0: a > $o,X1: a] :
( ( vAPP(a,sTfun(a,$o),sK13,X1) = X0 )
| ( $false = vAPP(sTfun(a,$o),$o,sK8,X0) )
| ( $false = vAPP(a,$o,X0,X1) ) ),
inference(trivial_inequality_removal,[],[f108]) ).
thf(f108,plain,
! [X0: a > $o,X1: a] :
( ( $true != $true )
| ( vAPP(a,sTfun(a,$o),sK13,X1) = X0 )
| ( $false = vAPP(sTfun(a,$o),$o,sK8,X0) )
| ( $false = vAPP(a,$o,X0,X1) ) ),
inference(superposition,[],[f85,f4]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f85,plain,
! [X0: a > $o,X1: a] :
( ( $true != vAPP(a,$o,X0,X1) )
| ( vAPP(a,sTfun(a,$o),sK13,X1) = X0 )
| ( $false = vAPP(sTfun(a,$o),$o,sK8,X0) ) ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f83,plain,
! [X0: a > $o,X1: a] :
( ( $true != $true )
| ( $true != vAPP(a,$o,X0,X1) )
| ( vAPP(a,sTfun(a,$o),sK13,X1) = X0 )
| ( $false = vAPP(sTfun(a,$o),$o,sK8,X0) ) ),
inference(superposition,[],[f44,f4]) ).
thf(f44,plain,
! [X9: a > $o,X7: a] :
( ( $true != vAPP(sTfun(a,$o),$o,sK8,X9) )
| ( $true != vAPP(a,$o,X9,X7) )
| ( vAPP(a,sTfun(a,$o),sK13,X7) = X9 ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f31,plain,
( ( ( ! [X4: a > $o] :
( ( $true != vAPP(a,$o,X4,sK11) )
| ( $true != vAPP(a,$o,X4,sK9) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X4) ) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,sK8),sK10),sK11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,sK8),sK9),sK10) ) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,sK8) )
| ! [X6: a > $o] :
( ( $true != vAPP(a,$o,X6,sK12) )
| ( $true != vAPP(a,$o,X6,sK12) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X6) ) ) )
& ! [X7: a] :
( ! [X9: a > $o] :
( ( vAPP(a,sTfun(a,$o),sK13,X7) = X9 )
| ( $true != vAPP(a,$o,X9,X7) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X9) ) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK13,X7),X7) )
& ( $true = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),sK13,X7)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12,sK13])],[f26,f30,f29,f28,f27]) ).
thf(f27,plain,
( ? [X0: ( a > $o ) > $o] :
( ( ? [X1: a,X2: a,X3: a] :
( ! [X4: a > $o] :
( ( $true != vAPP(a,$o,X4,X3) )
| ( vAPP(a,$o,X4,X1) != $true )
| ( vAPP(sTfun(a,$o),$o,X0,X4) != $true ) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,X0),X2),X3) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,X0),X1),X2) ) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,X0) )
| ? [X5: a] :
! [X6: a > $o] :
( ( $true != vAPP(a,$o,X6,X5) )
| ( $true != vAPP(a,$o,X6,X5) )
| ( $true != vAPP(sTfun(a,$o),$o,X0,X6) ) ) )
& ! [X7: a] :
? [X8: a > $o] :
( ! [X9: a > $o] :
( ( X8 = X9 )
| ( $true != vAPP(a,$o,X9,X7) )
| ( $true != vAPP(sTfun(a,$o),$o,X0,X9) ) )
& ( $true = vAPP(a,$o,X8,X7) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X8) ) ) )
=> ( ( ? [X3: a,X2: a,X1: a] :
( ! [X4: a > $o] :
( ( $true != vAPP(a,$o,X4,X3) )
| ( vAPP(a,$o,X4,X1) != $true )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X4) ) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,sK8),X2),X3) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,sK8),X1),X2) ) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,sK8) )
| ? [X5: a] :
! [X6: a > $o] :
( ( $true != vAPP(a,$o,X6,X5) )
| ( $true != vAPP(a,$o,X6,X5) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X6) ) ) )
& ! [X7: a] :
? [X8: a > $o] :
( ! [X9: a > $o] :
( ( X8 = X9 )
| ( $true != vAPP(a,$o,X9,X7) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X9) ) )
& ( $true = vAPP(a,$o,X8,X7) )
& ( $true = vAPP(sTfun(a,$o),$o,sK8,X8) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f28,plain,
( ? [X3: a,X2: a,X1: a] :
( ! [X4: a > $o] :
( ( $true != vAPP(a,$o,X4,X3) )
| ( vAPP(a,$o,X4,X1) != $true )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X4) ) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,sK8),X2),X3) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,sK8),X1),X2) ) )
=> ( ! [X4: a > $o] :
( ( $true != vAPP(a,$o,X4,sK11) )
| ( $true != vAPP(a,$o,X4,sK9) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X4) ) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,sK8),sK10),sK11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,sK8),sK9),sK10) ) ) ),
introduced(choice_axiom,[]) ).
thf(f29,plain,
( ? [X5: a] :
! [X6: a > $o] :
( ( $true != vAPP(a,$o,X6,X5) )
| ( $true != vAPP(a,$o,X6,X5) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X6) ) )
=> ! [X6: a > $o] :
( ( $true != vAPP(a,$o,X6,sK12) )
| ( $true != vAPP(a,$o,X6,sK12) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X6) ) ) ),
introduced(choice_axiom,[]) ).
thf(f30,plain,
! [X7: a] :
( ? [X8: a > $o] :
( ! [X9: a > $o] :
( ( X8 = X9 )
| ( $true != vAPP(a,$o,X9,X7) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X9) ) )
& ( $true = vAPP(a,$o,X8,X7) )
& ( $true = vAPP(sTfun(a,$o),$o,sK8,X8) ) )
=> ( ! [X9: a > $o] :
( ( vAPP(a,sTfun(a,$o),sK13,X7) = X9 )
| ( $true != vAPP(a,$o,X9,X7) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X9) ) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK13,X7),X7) )
& ( $true = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),sK13,X7)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f26,plain,
? [X0: ( a > $o ) > $o] :
( ( ? [X1: a,X2: a,X3: a] :
( ! [X4: a > $o] :
( ( $true != vAPP(a,$o,X4,X3) )
| ( vAPP(a,$o,X4,X1) != $true )
| ( vAPP(sTfun(a,$o),$o,X0,X4) != $true ) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,X0),X2),X3) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,X0),X1),X2) ) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,X0) )
| ? [X5: a] :
! [X6: a > $o] :
( ( $true != vAPP(a,$o,X6,X5) )
| ( $true != vAPP(a,$o,X6,X5) )
| ( $true != vAPP(sTfun(a,$o),$o,X0,X6) ) ) )
& ! [X7: a] :
? [X8: a > $o] :
( ! [X9: a > $o] :
( ( X8 = X9 )
| ( $true != vAPP(a,$o,X9,X7) )
| ( $true != vAPP(sTfun(a,$o),$o,X0,X9) ) )
& ( $true = vAPP(a,$o,X8,X7) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X8) ) ) ),
inference(rectify,[],[f12]) ).
thf(f12,plain,
? [X0: ( a > $o ) > $o] :
( ( ? [X4: a,X5: a,X6: a] :
( ! [X9: a > $o] :
( ( $true != vAPP(a,$o,X9,X6) )
| ( $true != vAPP(a,$o,X9,X4) )
| ( $true != vAPP(sTfun(a,$o),$o,X0,X9) ) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,X0),X5),X6) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,X0),X4),X5) ) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,X0) )
| ? [X14: a] :
! [X15: a > $o] :
( ( $true != vAPP(a,$o,X15,X14) )
| ( $true != vAPP(a,$o,X15,X14) )
| ( $true != vAPP(sTfun(a,$o),$o,X0,X15) ) ) )
& ! [X1: a] :
? [X2: a > $o] :
( ! [X3: a > $o] :
( ( X2 = X3 )
| ( vAPP(a,$o,X3,X1) != $true )
| ( vAPP(sTfun(a,$o),$o,X0,X3) != $true ) )
& ( vAPP(a,$o,X2,X1) = $true )
& ( vAPP(sTfun(a,$o),$o,X0,X2) = $true ) ) ),
inference(definition_folding,[],[f8,f11,f10,f9]) ).
thf(f9,plain,
! [X5: a,X4: a,X0: ( a > $o ) > $o] :
( ? [X8: a > $o] :
( ( $true = vAPP(a,$o,X8,X5) )
& ( $true = vAPP(a,$o,X8,X4) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X8) ) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,X0),X4),X5) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f10,plain,
! [X6: a,X5: a,X0: ( a > $o ) > $o] :
( ? [X7: a > $o] :
( ( $true = vAPP(a,$o,X7,X6) )
& ( $true = vAPP(a,$o,X7,X5) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X7) ) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,X0),X5),X6) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f11,plain,
! [X0: ( a > $o ) > $o] :
( ? [X10: a,X11: a] :
( ! [X13: a > $o] :
( ( $true != vAPP(a,$o,X13,X10) )
| ( $true != vAPP(a,$o,X13,X11) )
| ( $true != vAPP(sTfun(a,$o),$o,X0,X13) ) )
& ? [X12: a > $o] :
( ( $true = vAPP(a,$o,X12,X11) )
& ( $true = vAPP(a,$o,X12,X10) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X12) ) ) )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f8,plain,
? [X0: ( a > $o ) > $o] :
( ( ? [X4: a,X5: a,X6: a] :
( ! [X9: a > $o] :
( ( $true != vAPP(a,$o,X9,X6) )
| ( $true != vAPP(a,$o,X9,X4) )
| ( $true != vAPP(sTfun(a,$o),$o,X0,X9) ) )
& ? [X7: a > $o] :
( ( $true = vAPP(a,$o,X7,X6) )
& ( $true = vAPP(a,$o,X7,X5) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X7) ) )
& ? [X8: a > $o] :
( ( $true = vAPP(a,$o,X8,X5) )
& ( $true = vAPP(a,$o,X8,X4) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X8) ) ) )
| ? [X10: a,X11: a] :
( ! [X13: a > $o] :
( ( $true != vAPP(a,$o,X13,X10) )
| ( $true != vAPP(a,$o,X13,X11) )
| ( $true != vAPP(sTfun(a,$o),$o,X0,X13) ) )
& ? [X12: a > $o] :
( ( $true = vAPP(a,$o,X12,X11) )
& ( $true = vAPP(a,$o,X12,X10) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X12) ) ) )
| ? [X14: a] :
! [X15: a > $o] :
( ( $true != vAPP(a,$o,X15,X14) )
| ( $true != vAPP(a,$o,X15,X14) )
| ( $true != vAPP(sTfun(a,$o),$o,X0,X15) ) ) )
& ! [X1: a] :
? [X2: a > $o] :
( ! [X3: a > $o] :
( ( X2 = X3 )
| ( vAPP(a,$o,X3,X1) != $true )
| ( vAPP(sTfun(a,$o),$o,X0,X3) != $true ) )
& ( vAPP(a,$o,X2,X1) = $true )
& ( vAPP(sTfun(a,$o),$o,X0,X2) = $true ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
? [X0: ( a > $o ) > $o] :
( ( ? [X4: a,X5: a,X6: a] :
( ! [X9: a > $o] :
( ( $true != vAPP(a,$o,X9,X6) )
| ( $true != vAPP(a,$o,X9,X4) )
| ( $true != vAPP(sTfun(a,$o),$o,X0,X9) ) )
& ? [X7: a > $o] :
( ( $true = vAPP(a,$o,X7,X6) )
& ( $true = vAPP(a,$o,X7,X5) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X7) ) )
& ? [X8: a > $o] :
( ( $true = vAPP(a,$o,X8,X5) )
& ( $true = vAPP(a,$o,X8,X4) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X8) ) ) )
| ? [X10: a,X11: a] :
( ! [X13: a > $o] :
( ( $true != vAPP(a,$o,X13,X10) )
| ( $true != vAPP(a,$o,X13,X11) )
| ( $true != vAPP(sTfun(a,$o),$o,X0,X13) ) )
& ? [X12: a > $o] :
( ( $true = vAPP(a,$o,X12,X11) )
& ( $true = vAPP(a,$o,X12,X10) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X12) ) ) )
| ? [X14: a] :
! [X15: a > $o] :
( ( $true != vAPP(a,$o,X15,X14) )
| ( $true != vAPP(a,$o,X15,X14) )
| ( $true != vAPP(sTfun(a,$o),$o,X0,X15) ) ) )
& ! [X1: a] :
? [X2: a > $o] :
( ! [X3: a > $o] :
( ( X2 = X3 )
| ( vAPP(a,$o,X3,X1) != $true )
| ( vAPP(sTfun(a,$o),$o,X0,X3) != $true ) )
& ( vAPP(a,$o,X2,X1) = $true )
& ( vAPP(sTfun(a,$o),$o,X0,X2) = $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ! [X0: ( a > $o ) > $o] :
( ! [X1: a] :
? [X2: a > $o] :
( ! [X3: a > $o] :
( ( ( vAPP(a,$o,X3,X1) = $true )
& ( vAPP(sTfun(a,$o),$o,X0,X3) = $true ) )
=> ( X2 = X3 ) )
& ( vAPP(a,$o,X2,X1) = $true )
& ( vAPP(sTfun(a,$o),$o,X0,X2) = $true ) )
=> ( ! [X4: a,X5: a,X6: a] :
( ( ? [X7: a > $o] :
( ( $true = vAPP(a,$o,X7,X6) )
& ( $true = vAPP(a,$o,X7,X5) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X7) ) )
& ? [X8: a > $o] :
( ( $true = vAPP(a,$o,X8,X5) )
& ( $true = vAPP(a,$o,X8,X4) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X8) ) ) )
=> ? [X9: a > $o] :
( ( $true = vAPP(a,$o,X9,X6) )
& ( $true = vAPP(a,$o,X9,X4) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X9) ) ) )
& ! [X10: a,X11: a] :
( ? [X12: a > $o] :
( ( $true = vAPP(a,$o,X12,X11) )
& ( $true = vAPP(a,$o,X12,X10) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X12) ) )
=> ? [X13: a > $o] :
( ( $true = vAPP(a,$o,X13,X10) )
& ( $true = vAPP(a,$o,X13,X11) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X13) ) ) )
& ! [X14: a] :
? [X15: a > $o] :
( ( $true = vAPP(a,$o,X15,X14) )
& ( $true = vAPP(a,$o,X15,X14) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X15) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ! [X0: ( a > $o ) > $o] :
( ! [X1: a] :
? [X2: a > $o] :
( ! [X3: a > $o] :
( ( vAPP(a,$o,X3,X1)
& vAPP(sTfun(a,$o),$o,X0,X3) )
=> ( X2 = X3 ) )
& vAPP(a,$o,X2,X1)
& vAPP(sTfun(a,$o),$o,X0,X2) )
=> ( ! [X4: a,X5: a,X6: a] :
( ( ? [X7: a > $o] :
( vAPP(a,$o,X7,X6)
& vAPP(a,$o,X7,X5)
& vAPP(sTfun(a,$o),$o,X0,X7) )
& ? [X8: a > $o] :
( vAPP(a,$o,X8,X5)
& vAPP(a,$o,X8,X4)
& vAPP(sTfun(a,$o),$o,X0,X8) ) )
=> ? [X9: a > $o] :
( vAPP(a,$o,X9,X6)
& vAPP(a,$o,X9,X4)
& vAPP(sTfun(a,$o),$o,X0,X9) ) )
& ! [X10: a,X11: a] :
( ? [X12: a > $o] :
( vAPP(a,$o,X12,X11)
& vAPP(a,$o,X12,X10)
& vAPP(sTfun(a,$o),$o,X0,X12) )
=> ? [X13: a > $o] :
( vAPP(a,$o,X13,X10)
& vAPP(a,$o,X13,X11)
& vAPP(sTfun(a,$o),$o,X0,X13) ) )
& ! [X14: a] :
? [X15: a > $o] :
( vAPP(a,$o,X15,X14)
& vAPP(a,$o,X15,X14)
& vAPP(sTfun(a,$o),$o,X0,X15) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > $o ) > $o] :
( ! [X1: a] :
? [X2: a > $o] :
( ! [X3: a > $o] :
( ( vAPP(a,$o,X3,X1)
& vAPP(sTfun(a,$o),$o,X0,X3) )
=> ( X2 = X3 ) )
& vAPP(a,$o,X2,X1)
& vAPP(sTfun(a,$o),$o,X0,X2) )
=> ( ! [X1: a,X5: a,X6: a] :
( ( ? [X4: a > $o] :
( vAPP(a,$o,X4,X6)
& vAPP(a,$o,X4,X5)
& vAPP(sTfun(a,$o),$o,X0,X4) )
& ? [X4: a > $o] :
( vAPP(a,$o,X4,X5)
& vAPP(a,$o,X4,X1)
& vAPP(sTfun(a,$o),$o,X0,X4) ) )
=> ? [X4: a > $o] :
( vAPP(a,$o,X4,X6)
& vAPP(a,$o,X4,X1)
& vAPP(sTfun(a,$o),$o,X0,X4) ) )
& ! [X1: a,X5: a] :
( ? [X4: a > $o] :
( vAPP(a,$o,X4,X5)
& vAPP(a,$o,X4,X1)
& vAPP(sTfun(a,$o),$o,X0,X4) )
=> ? [X4: a > $o] :
( vAPP(a,$o,X4,X1)
& vAPP(a,$o,X4,X5)
& vAPP(sTfun(a,$o),$o,X0,X4) ) )
& ! [X1: a] :
? [X4: a > $o] :
( vAPP(a,$o,X4,X1)
& vAPP(a,$o,X4,X1)
& vAPP(sTfun(a,$o),$o,X0,X4) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: ( a > $o ) > $o] :
( ! [X1: a] :
? [X2: a > $o] :
( ! [X3: a > $o] :
( ( vAPP(a,$o,X3,X1)
& vAPP(sTfun(a,$o),$o,X0,X3) )
=> ( X2 = X3 ) )
& vAPP(a,$o,X2,X1)
& vAPP(sTfun(a,$o),$o,X0,X2) )
=> ( ! [X1: a,X5: a,X6: a] :
( ( ? [X4: a > $o] :
( vAPP(a,$o,X4,X6)
& vAPP(a,$o,X4,X5)
& vAPP(sTfun(a,$o),$o,X0,X4) )
& ? [X4: a > $o] :
( vAPP(a,$o,X4,X5)
& vAPP(a,$o,X4,X1)
& vAPP(sTfun(a,$o),$o,X0,X4) ) )
=> ? [X4: a > $o] :
( vAPP(a,$o,X4,X6)
& vAPP(a,$o,X4,X1)
& vAPP(sTfun(a,$o),$o,X0,X4) ) )
& ! [X1: a,X5: a] :
( ? [X4: a > $o] :
( vAPP(a,$o,X4,X5)
& vAPP(a,$o,X4,X1)
& vAPP(sTfun(a,$o),$o,X0,X4) )
=> ? [X4: a > $o] :
( vAPP(a,$o,X4,X1)
& vAPP(a,$o,X4,X5)
& vAPP(sTfun(a,$o),$o,X0,X4) ) )
& ! [X1: a] :
? [X4: a > $o] :
( vAPP(a,$o,X4,X1)
& vAPP(a,$o,X4,X1)
& vAPP(sTfun(a,$o),$o,X0,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM261_B_pme) ).
thf(f854,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK13,sK9),sK10) )
| ~ spl14_5
| ~ spl14_25 ),
inference(backward_demodulation,[],[f840,f712]) ).
thf(f712,plain,
( ( vAPP(a,sTfun(a,$o),sK13,sK9) = vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,sK8),sK9),sK10) )
| ~ spl14_25 ),
inference(avatar_component_clause,[],[f710]) ).
thf(f710,plain,
( spl14_25
<=> ( vAPP(a,sTfun(a,$o),sK13,sK9) = vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,sK8),sK9),sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_25])]) ).
thf(f840,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,sK8),sK9),sK10),sK10) )
| ~ spl14_5 ),
inference(trivial_inequality_removal,[],[f833]) ).
thf(f833,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,sK8),sK9),sK10),sK10) )
| ~ spl14_5 ),
inference(superposition,[],[f41,f70]) ).
thf(f70,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,sK8),sK9),sK10) )
| ~ spl14_5 ),
inference(avatar_component_clause,[],[f68]) ).
thf(f68,plain,
( spl14_5
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,sK8),sK9),sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_5])]) ).
thf(f41,plain,
! [X2: ( a > $o ) > $o,X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,X2),X1),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,X2),X1),X0),X0) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f25,plain,
! [X0: a,X1: a,X2: ( a > $o ) > $o] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,X2),X1),X0),X0) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,X2),X1),X0),X1) )
& ( $true = vAPP(sTfun(a,$o),$o,X2,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,X2),X1),X0)) ) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f23,f24]) ).
thf(f24,plain,
! [X0: a,X1: a,X2: ( a > $o ) > $o] :
( ? [X3: a > $o] :
( ( $true = vAPP(a,$o,X3,X0) )
& ( vAPP(a,$o,X3,X1) = $true )
& ( $true = vAPP(sTfun(a,$o),$o,X2,X3) ) )
=> ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,X2),X1),X0),X0) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,X2),X1),X0),X1) )
& ( $true = vAPP(sTfun(a,$o),$o,X2,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,X2),X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f23,plain,
! [X0: a,X1: a,X2: ( a > $o ) > $o] :
( ? [X3: a > $o] :
( ( $true = vAPP(a,$o,X3,X0) )
& ( vAPP(a,$o,X3,X1) = $true )
& ( $true = vAPP(sTfun(a,$o),$o,X2,X3) ) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,X2),X1),X0) ) ),
inference(rectify,[],[f22]) ).
thf(f22,plain,
! [X5: a,X4: a,X0: ( a > $o ) > $o] :
( ? [X8: a > $o] :
( ( $true = vAPP(a,$o,X8,X5) )
& ( $true = vAPP(a,$o,X8,X4) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X8) ) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,X0),X4),X5) ) ),
inference(nnf_transformation,[],[f9]) ).
thf(f800,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK13,sK10),sK11) )
| ~ spl14_4
| ~ spl14_23 ),
inference(backward_demodulation,[],[f792,f599]) ).
thf(f599,plain,
( ( vAPP(a,sTfun(a,$o),sK13,sK10) = vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,sK8),sK10),sK11) )
| ~ spl14_23 ),
inference(avatar_component_clause,[],[f597]) ).
thf(f597,plain,
( spl14_23
<=> ( vAPP(a,sTfun(a,$o),sK13,sK10) = vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,sK8),sK10),sK11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_23])]) ).
thf(f792,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,sK8),sK10),sK11),sK11) )
| ~ spl14_4 ),
inference(trivial_inequality_removal,[],[f783]) ).
thf(f783,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,sK8),sK10),sK11),sK11) )
| ~ spl14_4 ),
inference(superposition,[],[f38,f65]) ).
thf(f65,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,sK8),sK10),sK11) )
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f63]) ).
thf(f63,plain,
( spl14_4
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,sK8),sK10),sK11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_4])]) ).
thf(f38,plain,
! [X2: ( a > $o ) > $o,X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,X2),X1),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,X2),X1),X0),X0) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f21,plain,
! [X0: a,X1: a,X2: ( a > $o ) > $o] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,X2),X1),X0),X0) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,X2),X1),X0),X1) )
& ( $true = vAPP(sTfun(a,$o),$o,X2,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,X2),X1),X0)) ) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f19,f20]) ).
thf(f20,plain,
! [X0: a,X1: a,X2: ( a > $o ) > $o] :
( ? [X3: a > $o] :
( ( $true = vAPP(a,$o,X3,X0) )
& ( vAPP(a,$o,X3,X1) = $true )
& ( $true = vAPP(sTfun(a,$o),$o,X2,X3) ) )
=> ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,X2),X1),X0),X0) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,X2),X1),X0),X1) )
& ( $true = vAPP(sTfun(a,$o),$o,X2,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,X2),X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f19,plain,
! [X0: a,X1: a,X2: ( a > $o ) > $o] :
( ? [X3: a > $o] :
( ( $true = vAPP(a,$o,X3,X0) )
& ( vAPP(a,$o,X3,X1) = $true )
& ( $true = vAPP(sTfun(a,$o),$o,X2,X3) ) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,X2),X1),X0) ) ),
inference(rectify,[],[f18]) ).
thf(f18,plain,
! [X6: a,X5: a,X0: ( a > $o ) > $o] :
( ? [X7: a > $o] :
( ( $true = vAPP(a,$o,X7,X6) )
& ( $true = vAPP(a,$o,X7,X5) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X7) ) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,X0),X5),X6) ) ),
inference(nnf_transformation,[],[f10]) ).
thf(f856,plain,
( ~ spl14_19
| spl14_24
| ~ spl14_25 ),
inference(avatar_split_clause,[],[f855,f710,f706,f321]) ).
thf(f706,plain,
( spl14_24
<=> ( $false = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,sK8),sK9),sK10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_24])]) ).
thf(f855,plain,
( ( $false != vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),sK13,sK9)) )
| spl14_24
| ~ spl14_25 ),
inference(forward_demodulation,[],[f707,f712]) ).
thf(f707,plain,
( ( $false != vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,sK8),sK9),sK10)) )
| spl14_24 ),
inference(avatar_component_clause,[],[f706]) ).
thf(f845,plain,
( ~ spl14_5
| ~ spl14_24 ),
inference(avatar_contradiction_clause,[],[f844]) ).
thf(f844,plain,
( $false
| ~ spl14_5
| ~ spl14_24 ),
inference(trivial_inequality_removal,[],[f843]) ).
thf(f843,plain,
( ( $true = $false )
| ~ spl14_5
| ~ spl14_24 ),
inference(forward_demodulation,[],[f841,f708]) ).
thf(f708,plain,
( ( $false = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,sK8),sK9),sK10)) )
| ~ spl14_24 ),
inference(avatar_component_clause,[],[f706]) ).
thf(f841,plain,
( ( $true = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,sK8),sK9),sK10)) )
| ~ spl14_5 ),
inference(trivial_inequality_removal,[],[f832]) ).
thf(f832,plain,
( ( $true != $true )
| ( $true = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,sK8),sK9),sK10)) )
| ~ spl14_5 ),
inference(superposition,[],[f39,f70]) ).
thf(f39,plain,
! [X2: ( a > $o ) > $o,X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,X2),X1),X0) )
| ( $true = vAPP(sTfun(a,$o),$o,X2,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,X2),X1),X0)) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f797,plain,
( ~ spl14_4
| ~ spl14_22 ),
inference(avatar_contradiction_clause,[],[f796]) ).
thf(f796,plain,
( $false
| ~ spl14_4
| ~ spl14_22 ),
inference(trivial_inequality_removal,[],[f795]) ).
thf(f795,plain,
( ( $true = $false )
| ~ spl14_4
| ~ spl14_22 ),
inference(forward_demodulation,[],[f793,f595]) ).
thf(f595,plain,
( ( $false = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,sK8),sK10),sK11)) )
| ~ spl14_22 ),
inference(avatar_component_clause,[],[f593]) ).
thf(f593,plain,
( spl14_22
<=> ( $false = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,sK8),sK10),sK11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_22])]) ).
thf(f793,plain,
( ( $true = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,sK8),sK10),sK11)) )
| ~ spl14_4 ),
inference(trivial_inequality_removal,[],[f782]) ).
thf(f782,plain,
( ( $true != $true )
| ( $true = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,sK8),sK10),sK11)) )
| ~ spl14_4 ),
inference(superposition,[],[f36,f65]) ).
thf(f36,plain,
! [X2: ( a > $o ) > $o,X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,X2),X1),X0) )
| ( $true = vAPP(sTfun(a,$o),$o,X2,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,X2),X1),X0)) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f745,plain,
~ spl14_2,
inference(avatar_contradiction_clause,[],[f744]) ).
thf(f744,plain,
( $false
| ~ spl14_2 ),
inference(subsumption_resolution,[],[f743,f611]) ).
thf(f611,plain,
( ( $true = vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,sK8),vAPP(sTfun(sTfun(a,$o),$o),a,sK3,sK8)) )
| ~ spl14_2 ),
inference(trivial_inequality_removal,[],[f608]) ).
thf(f608,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,sK8),vAPP(sTfun(sTfun(a,$o),$o),a,sK3,sK8)) )
| ~ spl14_2 ),
inference(superposition,[],[f33,f57]) ).
thf(f57,plain,
( ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,sK8) )
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f55,plain,
( spl14_2
<=> ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_2])]) ).
thf(f33,plain,
! [X0: ( a > $o ) > $o] :
( ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,X0) )
| ( $true = vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,X0),vAPP(sTfun(sTfun(a,$o),$o),a,sK3,X0)) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f17,plain,
! [X0: ( a > $o ) > $o] :
( ( ! [X3: a > $o] :
( ( $true != vAPP(a,$o,X3,vAPP(sTfun(sTfun(a,$o),$o),a,sK3,X0)) )
| ( $true != vAPP(a,$o,X3,vAPP(sTfun(sTfun(a,$o),$o),a,sK4,X0)) )
| ( vAPP(sTfun(a,$o),$o,X0,X3) != $true ) )
& ( $true = vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,X0),vAPP(sTfun(sTfun(a,$o),$o),a,sK4,X0)) )
& ( $true = vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,X0),vAPP(sTfun(sTfun(a,$o),$o),a,sK3,X0)) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,X0)) ) )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f14,f16,f15]) ).
thf(f15,plain,
! [X0: ( a > $o ) > $o] :
( ? [X1: a,X2: a] :
( ! [X3: a > $o] :
( ( vAPP(a,$o,X3,X1) != $true )
| ( $true != vAPP(a,$o,X3,X2) )
| ( vAPP(sTfun(a,$o),$o,X0,X3) != $true ) )
& ? [X4: a > $o] :
( ( $true = vAPP(a,$o,X4,X2) )
& ( vAPP(a,$o,X4,X1) = $true )
& ( vAPP(sTfun(a,$o),$o,X0,X4) = $true ) ) )
=> ( ! [X3: a > $o] :
( ( $true != vAPP(a,$o,X3,vAPP(sTfun(sTfun(a,$o),$o),a,sK3,X0)) )
| ( $true != vAPP(a,$o,X3,vAPP(sTfun(sTfun(a,$o),$o),a,sK4,X0)) )
| ( vAPP(sTfun(a,$o),$o,X0,X3) != $true ) )
& ? [X4: a > $o] :
( ( $true = vAPP(a,$o,X4,vAPP(sTfun(sTfun(a,$o),$o),a,sK4,X0)) )
& ( $true = vAPP(a,$o,X4,vAPP(sTfun(sTfun(a,$o),$o),a,sK3,X0)) )
& ( vAPP(sTfun(a,$o),$o,X0,X4) = $true ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f16,plain,
! [X0: ( a > $o ) > $o] :
( ? [X4: a > $o] :
( ( $true = vAPP(a,$o,X4,vAPP(sTfun(sTfun(a,$o),$o),a,sK4,X0)) )
& ( $true = vAPP(a,$o,X4,vAPP(sTfun(sTfun(a,$o),$o),a,sK3,X0)) )
& ( vAPP(sTfun(a,$o),$o,X0,X4) = $true ) )
=> ( ( $true = vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,X0),vAPP(sTfun(sTfun(a,$o),$o),a,sK4,X0)) )
& ( $true = vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,X0),vAPP(sTfun(sTfun(a,$o),$o),a,sK3,X0)) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f14,plain,
! [X0: ( a > $o ) > $o] :
( ? [X1: a,X2: a] :
( ! [X3: a > $o] :
( ( vAPP(a,$o,X3,X1) != $true )
| ( $true != vAPP(a,$o,X3,X2) )
| ( vAPP(sTfun(a,$o),$o,X0,X3) != $true ) )
& ? [X4: a > $o] :
( ( $true = vAPP(a,$o,X4,X2) )
& ( vAPP(a,$o,X4,X1) = $true )
& ( vAPP(sTfun(a,$o),$o,X0,X4) = $true ) ) )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,X0) ) ),
inference(rectify,[],[f13]) ).
thf(f13,plain,
! [X0: ( a > $o ) > $o] :
( ? [X10: a,X11: a] :
( ! [X13: a > $o] :
( ( $true != vAPP(a,$o,X13,X10) )
| ( $true != vAPP(a,$o,X13,X11) )
| ( $true != vAPP(sTfun(a,$o),$o,X0,X13) ) )
& ? [X12: a > $o] :
( ( $true = vAPP(a,$o,X12,X11) )
& ( $true = vAPP(a,$o,X12,X10) )
& ( $true = vAPP(sTfun(a,$o),$o,X0,X12) ) ) )
| ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,X0) ) ),
inference(nnf_transformation,[],[f11]) ).
thf(f743,plain,
( ( $true != vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,sK8),vAPP(sTfun(sTfun(a,$o),$o),a,sK3,sK8)) )
| ~ spl14_2 ),
inference(subsumption_resolution,[],[f740,f610]) ).
thf(f610,plain,
( ( $true = vAPP(sTfun(a,$o),$o,sK8,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,sK8)) )
| ~ spl14_2 ),
inference(trivial_inequality_removal,[],[f609]) ).
thf(f609,plain,
( ( $true != $true )
| ( $true = vAPP(sTfun(a,$o),$o,sK8,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,sK8)) )
| ~ spl14_2 ),
inference(superposition,[],[f32,f57]) ).
thf(f32,plain,
! [X0: ( a > $o ) > $o] :
( ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,X0) )
| ( $true = vAPP(sTfun(a,$o),$o,X0,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,X0)) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f740,plain,
( ( $true != vAPP(sTfun(a,$o),$o,sK8,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,sK8)) )
| ( $true != vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,sK8),vAPP(sTfun(sTfun(a,$o),$o),a,sK3,sK8)) )
| ~ spl14_2 ),
inference(trivial_inequality_removal,[],[f734]) ).
thf(f734,plain,
( ( $true != $true )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,sK8)) )
| ( $true != vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,sK8),vAPP(sTfun(sTfun(a,$o),$o),a,sK3,sK8)) )
| ~ spl14_2 ),
inference(superposition,[],[f613,f612]) ).
thf(f612,plain,
( ( $true = vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,sK8),vAPP(sTfun(sTfun(a,$o),$o),a,sK4,sK8)) )
| ~ spl14_2 ),
inference(trivial_inequality_removal,[],[f607]) ).
thf(f607,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,sK8),vAPP(sTfun(sTfun(a,$o),$o),a,sK4,sK8)) )
| ~ spl14_2 ),
inference(superposition,[],[f34,f57]) ).
thf(f34,plain,
! [X0: ( a > $o ) > $o] :
( ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,X0) )
| ( $true = vAPP(a,$o,vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,$o),sK5,X0),vAPP(sTfun(sTfun(a,$o),$o),a,sK4,X0)) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f613,plain,
( ! [X0: a > $o] :
( ( $true != vAPP(a,$o,X0,vAPP(sTfun(sTfun(a,$o),$o),a,sK4,sK8)) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X0) )
| ( $true != vAPP(a,$o,X0,vAPP(sTfun(sTfun(a,$o),$o),a,sK3,sK8)) ) )
| ~ spl14_2 ),
inference(trivial_inequality_removal,[],[f606]) ).
thf(f606,plain,
( ! [X0: a > $o] :
( ( $true != $true )
| ( $true != vAPP(a,$o,X0,vAPP(sTfun(sTfun(a,$o),$o),a,sK4,sK8)) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X0) )
| ( $true != vAPP(a,$o,X0,vAPP(sTfun(sTfun(a,$o),$o),a,sK3,sK8)) ) )
| ~ spl14_2 ),
inference(superposition,[],[f35,f57]) ).
thf(f35,plain,
! [X3: a > $o,X0: ( a > $o ) > $o] :
( ( $true != vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,X0) )
| ( $true != vAPP(a,$o,X3,vAPP(sTfun(sTfun(a,$o),$o),a,sK4,X0)) )
| ( vAPP(sTfun(a,$o),$o,X0,X3) != $true )
| ( $true != vAPP(a,$o,X3,vAPP(sTfun(sTfun(a,$o),$o),a,sK3,X0)) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f720,plain,
( spl14_24
| spl14_25
| ~ spl14_5 ),
inference(avatar_split_clause,[],[f701,f68,f710,f706]) ).
thf(f701,plain,
( ( vAPP(a,sTfun(a,$o),sK13,sK9) = vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,sK8),sK9),sK10) )
| ( $false = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,sK8),sK9),sK10)) )
| ~ spl14_5 ),
inference(trivial_inequality_removal,[],[f700]) ).
thf(f700,plain,
( ( $true != $true )
| ( vAPP(a,sTfun(a,$o),sK13,sK9) = vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,sK8),sK9),sK10) )
| ( $false = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,sK8),sK9),sK10)) )
| ~ spl14_5 ),
inference(superposition,[],[f85,f487]) ).
thf(f487,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,sK8),sK9),sK10),sK9) )
| ~ spl14_5 ),
inference(trivial_inequality_removal,[],[f482]) ).
thf(f482,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,sK8),sK9),sK10),sK9) )
| ~ spl14_5 ),
inference(superposition,[],[f40,f70]) ).
thf(f40,plain,
! [X2: ( a > $o ) > $o,X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,X2),X1),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK7,X2),X1),X0),X1) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f602,plain,
( spl14_22
| spl14_23
| ~ spl14_4 ),
inference(avatar_split_clause,[],[f589,f63,f597,f593]) ).
thf(f589,plain,
( ( vAPP(a,sTfun(a,$o),sK13,sK10) = vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,sK8),sK10),sK11) )
| ( $false = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,sK8),sK10),sK11)) )
| ~ spl14_4 ),
inference(trivial_inequality_removal,[],[f588]) ).
thf(f588,plain,
( ( $true != $true )
| ( vAPP(a,sTfun(a,$o),sK13,sK10) = vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,sK8),sK10),sK11) )
| ( $false = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,sK8),sK10),sK11)) )
| ~ spl14_4 ),
inference(superposition,[],[f85,f478]) ).
thf(f478,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,sK8),sK10),sK11),sK10) )
| ~ spl14_4 ),
inference(trivial_inequality_removal,[],[f471]) ).
thf(f471,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,sK8),sK10),sK11),sK10) )
| ~ spl14_4 ),
inference(superposition,[],[f37,f65]) ).
thf(f37,plain,
! [X2: ( a > $o ) > $o,X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,X2),X1),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(a,sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,sTfun(a,$o))),sK6,X2),X1),X0),X1) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f324,plain,
( spl14_18
| spl14_19
| ~ spl14_3 ),
inference(avatar_split_clause,[],[f313,f59,f321,f317]) ).
thf(f59,plain,
( spl14_3
<=> ! [X4: a > $o] :
( ( $true != vAPP(a,$o,X4,sK11) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X4) )
| ( $true != vAPP(a,$o,X4,sK9) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_3])]) ).
thf(f313,plain,
( ( $false = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),sK13,sK9)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK13,sK9),sK11) )
| ~ spl14_3 ),
inference(trivial_inequality_removal,[],[f308]) ).
thf(f308,plain,
( ( $true != $true )
| ( $false = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),sK13,sK9)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK13,sK9),sK11) )
| ~ spl14_3 ),
inference(superposition,[],[f248,f43]) ).
thf(f43,plain,
! [X7: a] : ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK13,X7),X7) ),
inference(cnf_transformation,[],[f31]) ).
thf(f248,plain,
( ! [X0: a > $o] :
( ( $true != vAPP(a,$o,X0,sK9) )
| ( $false = vAPP(sTfun(a,$o),$o,sK8,X0) )
| ( $false = vAPP(a,$o,X0,sK11) ) )
| ~ spl14_3 ),
inference(trivial_inequality_removal,[],[f247]) ).
thf(f247,plain,
( ! [X0: a > $o] :
( ( $true != $true )
| ( $true != vAPP(a,$o,X0,sK9) )
| ( $false = vAPP(sTfun(a,$o),$o,sK8,X0) )
| ( $false = vAPP(a,$o,X0,sK11) ) )
| ~ spl14_3 ),
inference(superposition,[],[f191,f4]) ).
thf(f191,plain,
( ! [X0: a > $o] :
( ( $true != vAPP(a,$o,X0,sK11) )
| ( $true != vAPP(a,$o,X0,sK9) )
| ( $false = vAPP(sTfun(a,$o),$o,sK8,X0) ) )
| ~ spl14_3 ),
inference(trivial_inequality_removal,[],[f190]) ).
thf(f190,plain,
( ! [X0: a > $o] :
( ( $true != $true )
| ( $true != vAPP(a,$o,X0,sK11) )
| ( $true != vAPP(a,$o,X0,sK9) )
| ( $false = vAPP(sTfun(a,$o),$o,sK8,X0) ) )
| ~ spl14_3 ),
inference(superposition,[],[f60,f4]) ).
thf(f60,plain,
( ! [X4: a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,sK8,X4) )
| ( $true != vAPP(a,$o,X4,sK11) )
| ( $true != vAPP(a,$o,X4,sK9) ) )
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f186,plain,
~ spl14_1,
inference(avatar_contradiction_clause,[],[f185]) ).
thf(f185,plain,
( $false
| ~ spl14_1 ),
inference(trivial_inequality_removal,[],[f181]) ).
thf(f181,plain,
( ( $true != $true )
| ~ spl14_1 ),
inference(superposition,[],[f179,f43]) ).
thf(f179,plain,
( ! [X0: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK13,X0),sK12) )
| ~ spl14_1 ),
inference(trivial_inequality_removal,[],[f175]) ).
thf(f175,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK13,X0),sK12) ) )
| ~ spl14_1 ),
inference(superposition,[],[f53,f42]) ).
thf(f42,plain,
! [X7: a] : ( $true = vAPP(sTfun(a,$o),$o,sK8,vAPP(a,sTfun(a,$o),sK13,X7)) ),
inference(cnf_transformation,[],[f31]) ).
thf(f53,plain,
( ! [X6: a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,sK8,X6) )
| ( $true != vAPP(a,$o,X6,sK12) ) )
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f52,plain,
( spl14_1
<=> ! [X6: a > $o] :
( ( $true != vAPP(a,$o,X6,sK12) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X6) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_1])]) ).
thf(f71,plain,
( spl14_1
| spl14_2
| spl14_5 ),
inference(avatar_split_clause,[],[f48,f68,f55,f52]) ).
thf(f48,plain,
! [X6: a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,sK8),sK9),sK10) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,sK8) )
| ( $true != vAPP(a,$o,X6,sK12) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X6) ) ),
inference(duplicate_literal_removal,[],[f45]) ).
thf(f45,plain,
! [X6: a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP0,sK8),sK9),sK10) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,sK8) )
| ( $true != vAPP(a,$o,X6,sK12) )
| ( $true != vAPP(a,$o,X6,sK12) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X6) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f66,plain,
( spl14_1
| spl14_2
| spl14_4 ),
inference(avatar_split_clause,[],[f49,f63,f55,f52]) ).
thf(f49,plain,
! [X6: a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,sK8),sK10),sK11) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,sK8) )
| ( $true != vAPP(a,$o,X6,sK12) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X6) ) ),
inference(duplicate_literal_removal,[],[f46]) ).
thf(f46,plain,
! [X6: a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vAPP(sTfun(sTfun(a,$o),$o),sTfun(a,sTfun(a,$o)),sP1,sK8),sK10),sK11) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,sK8) )
| ( $true != vAPP(a,$o,X6,sK12) )
| ( $true != vAPP(a,$o,X6,sK12) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X6) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f61,plain,
( spl14_1
| spl14_2
| spl14_3 ),
inference(avatar_split_clause,[],[f50,f59,f55,f52]) ).
thf(f50,plain,
! [X6: a > $o,X4: a > $o] :
( ( $true != vAPP(a,$o,X4,sK11) )
| ( $true != vAPP(a,$o,X4,sK9) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X4) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,sK8) )
| ( $true != vAPP(a,$o,X6,sK12) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X6) ) ),
inference(duplicate_literal_removal,[],[f47]) ).
thf(f47,plain,
! [X6: a > $o,X4: a > $o] :
( ( $true != vAPP(a,$o,X4,sK11) )
| ( $true != vAPP(a,$o,X4,sK9) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X4) )
| ( $true = vAPP(sTfun(sTfun(a,$o),$o),$o,sP2,sK8) )
| ( $true != vAPP(a,$o,X6,sK12) )
| ( $true != vAPP(a,$o,X6,sK12) )
| ( $true != vAPP(sTfun(a,$o),$o,sK8,X6) ) ),
inference(cnf_transformation,[],[f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV009^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n007.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 11:56:20 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (9231)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (9234)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (9237)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (9238)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)
% 0.14/0.38 % (9239)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)
% 0.14/0.38 % (9235)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (9240)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)
% 0.14/0.38 % Exception at run slice level
% 0.14/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38 % (9236)WARNING: value z3 for option sas not known
% 0.14/0.38 % (9240)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.38 % Exception at run slice level
% 0.14/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38 % Exception at run slice level
% 0.14/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38 % (9236)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)
% 0.14/0.39 % (9251)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.14/0.39 % (9253)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)
% 0.14/0.40 % (9251)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.40 % (9253)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.40 % Exception at run slice level
% 0.14/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.40 % (9254)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)
% 0.14/0.41 % (9266)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.20/0.44 % (9254)First to succeed.
% 0.20/0.45 % (9254)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9231"
% 0.20/0.45 % (9254)Refutation found. Thanks to Tanya!
% 0.20/0.45 % SZS status Theorem for theBenchmark
% 0.20/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.46 % (9254)------------------------------
% 0.20/0.46 % (9254)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.46 % (9254)Termination reason: Refutation
% 0.20/0.46
% 0.20/0.46 % (9254)Memory used [KB]: 1115
% 0.20/0.46 % (9254)Time elapsed: 0.054 s
% 0.20/0.46 % (9254)Instructions burned: 71 (million)
% 0.20/0.46 % (9231)Success in time 0.094 s
%------------------------------------------------------------------------------