TSTP Solution File: ITP019^3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP019^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.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 : Mon May 20 22:44:30 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 73
% Syntax : Number of formulae : 190 ( 49 unt; 31 typ; 0 def)
% Number of atoms : 1240 ( 331 equ; 0 cnn)
% Maximal formula atoms : 30 ( 7 avg)
% Number of connectives : 442 ( 136 ~; 141 |; 71 &; 0 @)
% ( 69 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 65 ( 61 >; 4 *; 0 +; 0 <<)
% Number of symbols : 61 ( 58 usr; 32 con; 0-6 aty)
% Number of variables : 205 ( 0 ^ 183 !; 11 ?; 205 :)
% ( 11 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
tyop_2Enum_2Enum: $tType ).
thf(type_def_7,type,
tyop_2Erealax_2Ereal: $tType ).
thf(type_def_8,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
tyop_2Emin_2Ebool: $tType ).
thf(func_def_1,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
thf(func_def_2,type,
tyop_2Enum_2Enum: $tType ).
thf(func_def_3,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
thf(func_def_4,type,
tyop_2Erealax_2Ereal: $tType ).
thf(func_def_5,type,
c_2Ebool_2E_21:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_7,type,
c_2Enum_2E0: tyop_2Enum_2Enum ).
thf(func_def_8,type,
c_2Emin_2E_3D:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_9,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_10,type,
c_2Ebool_2E_3F:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
c_2Ebool_2EF: $o ).
thf(func_def_12,type,
c_2Ebool_2ET: $o ).
thf(func_def_13,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_14,type,
c_2Ecomplex_2Ecomplex__inv: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) > tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
thf(func_def_15,type,
c_2Ecomplex_2Ecomplex__of__num: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
thf(func_def_16,type,
c_2Ebool_2E_7E: $o > $o ).
thf(func_def_18,type,
vNOT: $o > $o ).
thf(func_def_21,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_22,type,
sK0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
thf(func_def_23,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_24,type,
sK2:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_26,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_27,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_28,type,
vAND: $o > $o > $o ).
thf(func_def_29,type,
vOR: $o > $o > $o ).
thf(func_def_30,type,
vIMP: $o > $o > $o ).
thf(f388,plain,
$false,
inference(avatar_sat_refutation,[],[f142,f147,f152,f156,f164,f199,f203,f208,f212,f216,f236,f240,f244,f251,f255,f280,f284,f288,f294,f329,f337,f341,f375,f379,f383,f387]) ).
thf(f387,plain,
( spl3_1
| ~ spl3_3
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f386,f381,f149,f139]) ).
thf(f139,plain,
( spl3_1
<=> ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = sK0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
thf(f149,plain,
( spl3_3
<=> ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
thf(f381,plain,
( spl3_26
<=> ! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X0 )
| ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).
thf(f386,plain,
( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = sK0 )
| ~ spl3_3
| ~ spl3_26 ),
inference(trivial_inequality_removal,[],[f384]) ).
thf(f384,plain,
( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) )
| ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = sK0 )
| ~ spl3_3
| ~ spl3_26 ),
inference(superposition,[],[f382,f151]) ).
thf(f151,plain,
( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,sK0) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f149]) ).
thf(f382,plain,
( ! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0) )
| ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X0 ) )
| ~ spl3_26 ),
inference(avatar_component_clause,[],[f381]) ).
thf(f383,plain,
spl3_26,
inference(avatar_split_clause,[],[f80,f381]) ).
thf(f80,plain,
! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X0 )
| ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f47,plain,
! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0) )
| ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != X0 ) )
& ( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X0 )
| ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0) ) ) ),
inference(nnf_transformation,[],[f38]) ).
thf(f38,plain,
! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0) )
<=> ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X0 ) ),
inference(rectify,[],[f11]) ).
thf(f11,axiom,
! [X6: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X6) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) )
<=> ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
thf(f379,plain,
spl3_25,
inference(avatar_split_clause,[],[f129,f377]) ).
thf(f377,plain,
( spl3_25
<=> ! [X0: $o] :
( ( $false = X0 )
| ( $false = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).
thf(f129,plain,
! [X0: $o] :
( ( $false = X0 )
| ( $false = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ),
inference(not_proxy_clausification,[],[f126]) ).
thf(f126,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $false = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ),
inference(binary_proxy_clausification,[],[f82]) ).
thf(f82,plain,
! [X0: $o] : ( vAPP($o,$o,vNOT,X0) = vAPP($o,$o,c_2Ebool_2E_7E,X0) ),
inference(cnf_transformation,[],[f21]) ).
thf(f21,plain,
! [X0: $o] : ( vAPP($o,$o,vNOT,X0) = vAPP($o,$o,c_2Ebool_2E_7E,X0) ),
inference(fool_elimination,[],[f20]) ).
thf(f20,plain,
! [X0: $o] :
( vAPP($o,$o,c_2Ebool_2E_7E,X0)
<=> vAPP($o,$o,vNOT,X0) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
! [X1: $o] :
( vAPP($o,$o,c_2Ebool_2E_7E,X1)
<=> vAPP($o,$o,vNOT,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_7E) ).
thf(f375,plain,
spl3_24,
inference(avatar_split_clause,[],[f118,f372]) ).
thf(f372,plain,
( spl3_24
<=> ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).
thf(f118,plain,
vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),
inference(equality_resolution,[],[f81]) ).
thf(f81,plain,
! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0) )
| ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != X0 ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f341,plain,
spl3_23,
inference(avatar_split_clause,[],[f86,f339]) ).
thf(f339,plain,
( spl3_23
<=> ! [X0: $tType,X1: X0 > $o] :
( ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK2(X0),X1)) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).
thf(f86,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK2(X0),X1)) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f55,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
| ! [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) ) )
& ( ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK2(X0),X1)) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f53,f54]) ).
thf(f54,plain,
! [X0: $tType,X1: X0 > $o] :
( ? [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) )
=> ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK2(X0),X1)) ) ),
introduced(choice_axiom,[]) ).
thf(f53,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
| ! [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) ) )
& ( ? [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) ) ) ),
inference(rectify,[],[f52]) ).
thf(f52,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
| ! [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) ) )
& ( ? [X2: X0] : ( $true = vAPP(X0,$o,X1,X2) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) ) ) ),
inference(nnf_transformation,[],[f27]) ).
thf(f27,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
<=> ? [X2: X0] : ( $true = vAPP(X0,$o,X1,X2) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f26,plain,
! [X0: $tType,X1: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1)
<=> ? [X2: X0] : vAPP(X0,$o,X1,X2) ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
! [X0: $tType,X3: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X3)
<=> ? [X4: X0] : vAPP(X0,$o,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_3F) ).
thf(f337,plain,
spl3_22,
inference(avatar_split_clause,[],[f85,f335]) ).
thf(f335,plain,
( spl3_22
<=> ! [X0: $tType,X1: X0 > $o] :
( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
| ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK1(X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).
thf(f85,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
| ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK1(X0),X1)) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f51,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
| ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK1(X0),X1)) ) )
& ( ! [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f49,f50]) ).
thf(f50,plain,
! [X0: $tType,X1: X0 > $o] :
( ? [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) )
=> ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK1(X0),X1)) ) ),
introduced(choice_axiom,[]) ).
thf(f49,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
| ? [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) ) )
& ( ! [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) ) ) ),
inference(rectify,[],[f48]) ).
thf(f48,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
| ? [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) ) )
& ( ! [X2: X0] : ( $true = vAPP(X0,$o,X1,X2) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) ) ) ),
inference(nnf_transformation,[],[f25]) ).
thf(f25,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
<=> ! [X2: X0] : ( $true = vAPP(X0,$o,X1,X2) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f24,plain,
! [X0: $tType,X1: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1)
<=> ! [X2: X0] : vAPP(X0,$o,X1,X2) ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
! [X0: $tType,X3: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X3)
<=> ! [X4: X0] : vAPP(X0,$o,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_21) ).
thf(f329,plain,
spl3_21,
inference(avatar_split_clause,[],[f91,f327]) ).
thf(f327,plain,
( spl3_21
<=> ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).
thf(f91,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f59,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) )
| ( ( $true != X1 )
& ( $true != X0 ) ) )
& ( ( $true = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) ) ) ),
inference(flattening,[],[f58]) ).
thf(f58,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) )
| ( ( $true != X1 )
& ( $true != X0 ) ) )
& ( ( $true = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) ) ) ),
inference(nnf_transformation,[],[f31]) ).
thf(f31,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) )
<=> ( ( $true = X1 )
| ( $true = X0 ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f30,plain,
! [X0: $o,X1: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1)
<=> ( X1
| X0 ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X1: $o,X2: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X1),X2)
<=> ( X2
| X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_5C_2F) ).
thf(f294,plain,
spl3_20,
inference(avatar_split_clause,[],[f128,f292]) ).
thf(f292,plain,
( spl3_20
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $true = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).
thf(f128,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $true = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ),
inference(not_proxy_clausification,[],[f127]) ).
thf(f127,plain,
! [X0: $o] :
( ( $false = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ),
inference(binary_proxy_clausification,[],[f82]) ).
thf(f288,plain,
spl3_19,
inference(avatar_split_clause,[],[f97,f286]) ).
thf(f286,plain,
( spl3_19
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).
thf(f97,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) != $true ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f62,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) = $true )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) != $true ) ) ),
inference(nnf_transformation,[],[f35]) ).
thf(f35,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) = $true )
<=> ( X1 = X2 ) ),
inference(fool_elimination,[],[f34]) ).
thf(f34,plain,
! [X0: $tType,X1: X0,X2: X0] :
( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2)
<=> ( X1 = X2 ) ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
! [X0: $tType,X1: X0,X2: X0] :
( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2)
<=> ( X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D) ).
thf(f284,plain,
spl3_18,
inference(avatar_split_clause,[],[f87,f282]) ).
thf(f282,plain,
( spl3_18
<=> ! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
| ( $true != vAPP(X0,$o,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).
thf(f87,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
| ( $true != vAPP(X0,$o,X1,X2) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f280,plain,
spl3_17,
inference(avatar_split_clause,[],[f84,f278]) ).
thf(f278,plain,
( spl3_17
<=> ! [X0: $tType,X1: X0 > $o,X3: X0] :
( ( $true = vAPP(X0,$o,X1,X3) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).
thf(f84,plain,
! [X0: $tType,X3: X0,X1: X0 > $o] :
( ( $true = vAPP(X0,$o,X1,X3) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f255,plain,
spl3_16,
inference(avatar_split_clause,[],[f124,f253]) ).
thf(f253,plain,
( spl3_16
<=> ! [X1: $o] :
( ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,$true),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
thf(f124,plain,
! [X1: $o] :
( ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,$true),X1) ) ),
inference(equality_resolution,[],[f94]) ).
thf(f94,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true != X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f61,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
| ( ( $true != X1 )
& ( $true = X0 ) ) )
& ( ( $true = X1 )
| ( $true != X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) ) ) ),
inference(flattening,[],[f60]) ).
thf(f60,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
| ( ( $true != X1 )
& ( $true = X0 ) ) )
& ( ( $true = X1 )
| ( $true != X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) ) ) ),
inference(nnf_transformation,[],[f42]) ).
thf(f42,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
<=> ( ( $true = X1 )
| ( $true != X0 ) ) ),
inference(ennf_transformation,[],[f33]) ).
thf(f33,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
<=> ( ( $true = X0 )
=> ( $true = X1 ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f32,plain,
! [X0: $o,X1: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1)
<=> ( X0
=> X1 ) ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
! [X1: $o,X2: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X1),X2)
<=> ( X1
=> X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D_3D_3E) ).
thf(f251,plain,
spl3_15,
inference(avatar_split_clause,[],[f95,f249]) ).
thf(f249,plain,
( spl3_15
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
| ( $true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).
thf(f95,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
| ( $true = X0 ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f244,plain,
spl3_14,
inference(avatar_split_clause,[],[f89,f242]) ).
thf(f242,plain,
( spl3_14
<=> ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
thf(f89,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f57,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) )
| ( $true != X1 )
| ( $true != X0 ) )
& ( ( ( $true = X1 )
& ( $true = X0 ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ) ),
inference(flattening,[],[f56]) ).
thf(f56,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) )
| ( $true != X1 )
| ( $true != X0 ) )
& ( ( ( $true = X1 )
& ( $true = X0 ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ) ),
inference(nnf_transformation,[],[f29]) ).
thf(f29,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) )
<=> ( ( $true = X1 )
& ( $true = X0 ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f28,plain,
! [X0: $o,X1: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1)
<=> ( X1
& X0 ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X1: $o,X2: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X1),X2)
<=> ( X2
& X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_2F_5C) ).
thf(f240,plain,
spl3_13,
inference(avatar_split_clause,[],[f88,f238]) ).
thf(f238,plain,
( spl3_13
<=> ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
thf(f88,plain,
! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f236,plain,
spl3_12,
inference(avatar_split_clause,[],[f125,f234]) ).
thf(f234,plain,
( spl3_12
<=> ! [X0: $tType,X2: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
thf(f125,plain,
! [X0: $tType,X2: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X2),X2) ),
inference(equality_resolution,[],[f98]) ).
thf(f98,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) = $true )
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f216,plain,
spl3_11,
inference(avatar_split_clause,[],[f123,f214]) ).
thf(f214,plain,
( spl3_11
<=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).
thf(f123,plain,
! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),$true) ),
inference(equality_resolution,[],[f96]) ).
thf(f96,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
| ( $true != X1 ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f212,plain,
spl3_10,
inference(avatar_split_clause,[],[f122,f210]) ).
thf(f210,plain,
( spl3_10
<=> ! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,$true),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
thf(f122,plain,
! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,$true),X1) ),
inference(equality_resolution,[],[f92]) ).
thf(f92,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) )
| ( $true != X0 ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f208,plain,
( spl3_9
| ~ spl3_4
| spl3_5 ),
inference(avatar_split_clause,[],[f176,f158,f154,f205]) ).
thf(f205,plain,
( spl3_9
<=> ( c_2Ebool_2EF = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
thf(f154,plain,
( spl3_4
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
thf(f158,plain,
( spl3_5
<=> ( c_2Ebool_2EF = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
thf(f176,plain,
( ( c_2Ebool_2EF = $false )
| ~ spl3_4
| spl3_5 ),
inference(trivial_inequality_removal,[],[f174]) ).
thf(f174,plain,
( ( $true != $true )
| ( c_2Ebool_2EF = $false )
| ~ spl3_4
| spl3_5 ),
inference(superposition,[],[f160,f155]) ).
thf(f155,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f154]) ).
thf(f160,plain,
( ( c_2Ebool_2EF != $true )
| spl3_5 ),
inference(avatar_component_clause,[],[f158]) ).
thf(f203,plain,
spl3_8,
inference(avatar_split_clause,[],[f121,f201]) ).
thf(f201,plain,
( spl3_8
<=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
thf(f121,plain,
! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),$true) ),
inference(equality_resolution,[],[f93]) ).
thf(f93,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) )
| ( $true != X1 ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f199,plain,
spl3_7,
inference(avatar_split_clause,[],[f120,f196]) ).
thf(f196,plain,
( spl3_7
<=> ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,$true),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
thf(f120,plain,
$true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,$true),$true),
inference(equality_resolution,[],[f119]) ).
thf(f119,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),$true) )
| ( $true != X0 ) ),
inference(equality_resolution,[],[f90]) ).
thf(f90,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) )
| ( $true != X1 )
| ( $true != X0 ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f164,plain,
( ~ spl3_5
| spl3_6 ),
inference(avatar_split_clause,[],[f130,f162,f158]) ).
thf(f162,plain,
( spl3_6
<=> ! [X0: $o] : ( $true = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
thf(f130,plain,
! [X0: $o] :
( ( $true = X0 )
| ( c_2Ebool_2EF != $true ) ),
inference(trivial_inequality_removal,[],[f103]) ).
thf(f103,plain,
! [X0: $o] :
( ( $true = X0 )
| ( c_2Ebool_2EF != $true )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f73,f99]) ).
thf(f99,plain,
c_2Ebool_2ET = $true,
inference(cnf_transformation,[],[f37]) ).
thf(f37,plain,
c_2Ebool_2ET = $true,
inference(fool_elimination,[],[f36]) ).
thf(f36,plain,
c_2Ebool_2ET,
inference(rectify,[],[f8]) ).
thf(f8,axiom,
c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(f73,plain,
! [X0: $o] :
( ( $true = X0 )
| ( c_2Ebool_2EF != $true )
| ( c_2Ebool_2ET != $true ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f46,plain,
! [X0: $o] :
( ( ( c_2Ebool_2EF = $true )
| ( $true != X0 )
| ( $true != vAPP($o,$o,vNOT,X0) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( ( c_2Ebool_2EF != $true )
& ( $true = X0 ) ) )
& ( ( $true = X0 )
| ( $true != X0 )
| ( c_2Ebool_2ET != $true ) )
& ( ( c_2Ebool_2ET = $true )
| ( ( $true != X0 )
& ( $true = X0 ) ) )
& ( ( $true = X0 )
| ( c_2Ebool_2EF != $true )
| ( c_2Ebool_2ET != $true ) )
& ( ( c_2Ebool_2ET = $true )
| ( ( $true != X0 )
& ( c_2Ebool_2EF = $true ) ) )
& ( ( c_2Ebool_2ET = $true )
| ( $true != X0 )
| ( c_2Ebool_2ET != $true ) )
& ( ( c_2Ebool_2ET = $true )
| ( ( c_2Ebool_2ET != $true )
& ( $true = X0 ) ) )
& ( ( $true = X0 )
| ( c_2Ebool_2ET != $true )
| ( $true != X0 ) )
& ( ( $true = X0 )
| ( ( $true != X0 )
& ( c_2Ebool_2ET = $true ) ) ) ),
inference(flattening,[],[f45]) ).
thf(f45,plain,
! [X0: $o] :
( ( ( c_2Ebool_2EF = $true )
| ( $true != X0 )
| ( $true != vAPP($o,$o,vNOT,X0) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( ( c_2Ebool_2EF != $true )
& ( $true = X0 ) ) )
& ( ( $true = X0 )
| ( $true != X0 )
| ( c_2Ebool_2ET != $true ) )
& ( ( c_2Ebool_2ET = $true )
| ( ( $true != X0 )
& ( $true = X0 ) ) )
& ( ( $true = X0 )
| ( c_2Ebool_2EF != $true )
| ( c_2Ebool_2ET != $true ) )
& ( ( c_2Ebool_2ET = $true )
| ( ( $true != X0 )
& ( c_2Ebool_2EF = $true ) ) )
& ( ( c_2Ebool_2ET = $true )
| ( $true != X0 )
| ( c_2Ebool_2ET != $true ) )
& ( ( c_2Ebool_2ET = $true )
| ( ( c_2Ebool_2ET != $true )
& ( $true = X0 ) ) )
& ( ( $true = X0 )
| ( c_2Ebool_2ET != $true )
| ( $true != X0 ) )
& ( ( $true = X0 )
| ( ( $true != X0 )
& ( c_2Ebool_2ET = $true ) ) ) ),
inference(nnf_transformation,[],[f41]) ).
thf(f41,plain,
! [X0: $o] :
( ( ( ( c_2Ebool_2EF = $true )
| ( $true != X0 ) )
<=> ( $true = vAPP($o,$o,vNOT,X0) ) )
& ( ( ( $true = X0 )
| ( $true != X0 ) )
<=> ( c_2Ebool_2ET = $true ) )
& ( ( ( $true = X0 )
| ( c_2Ebool_2EF != $true ) )
<=> ( c_2Ebool_2ET = $true ) )
& ( ( ( c_2Ebool_2ET = $true )
| ( $true != X0 ) )
<=> ( c_2Ebool_2ET = $true ) )
& ( ( ( $true = X0 )
| ( c_2Ebool_2ET != $true ) )
<=> ( $true = X0 ) ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f19,plain,
! [X0: $o] :
( ( ( ( $true = X0 )
=> ( c_2Ebool_2EF = $true ) )
<=> ( $true = vAPP($o,$o,vNOT,X0) ) )
& ( ( ( $true = X0 )
=> ( $true = X0 ) )
<=> ( c_2Ebool_2ET = $true ) )
& ( ( ( c_2Ebool_2EF = $true )
=> ( $true = X0 ) )
<=> ( c_2Ebool_2ET = $true ) )
& ( ( ( $true = X0 )
=> ( c_2Ebool_2ET = $true ) )
<=> ( c_2Ebool_2ET = $true ) )
& ( ( ( c_2Ebool_2ET = $true )
=> ( $true = X0 ) )
<=> ( $true = X0 ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f18,plain,
! [X0: $o] :
( ( ( X0
=> c_2Ebool_2EF )
<=> vAPP($o,$o,vNOT,X0) )
& ( ( X0
=> X0 )
<=> c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> X0 )
<=> c_2Ebool_2ET )
& ( ( X0
=> c_2Ebool_2ET )
<=> c_2Ebool_2ET )
& ( ( c_2Ebool_2ET
=> X0 )
<=> X0 ) ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
! [X5: $o] :
( ( ( X5
=> c_2Ebool_2EF )
<=> vAPP($o,$o,vNOT,X5) )
& ( ( X5
=> X5 )
<=> c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> X5 )
<=> c_2Ebool_2ET )
& ( ( X5
=> c_2Ebool_2ET )
<=> c_2Ebool_2ET )
& ( ( c_2Ebool_2ET
=> X5 )
<=> X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).
thf(f156,plain,
spl3_4,
inference(avatar_split_clause,[],[f15,f154]) ).
thf(f15,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f152,plain,
spl3_3,
inference(avatar_split_clause,[],[f137,f149]) ).
thf(f137,plain,
vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,sK0),
inference(equality_proxy_clausification,[],[f136]) ).
thf(f136,plain,
$true = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,sK0)),
inference(not_proxy_clausification,[],[f64]) ).
thf(f64,plain,
$true != vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,sK0))),
inference(cnf_transformation,[],[f44]) ).
thf(f44,plain,
( ( $true != vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,sK0))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),sK0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f40,f43]) ).
thf(f43,plain,
( ? [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( $true != vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),X0)) ) )
=> ( ( $true != vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,sK0))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),sK0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f40,plain,
? [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( $true != vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),X0)) ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f17,plain,
~ ! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( ( $true = vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),X0)) )
=> ( $true = vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0))) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f16,plain,
~ ! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X0)
=> vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0)) ),
inference(rectify,[],[f13]) ).
thf(f13,negated_conjecture,
~ ! [X6: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X6)
=> vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X6) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) ),
inference(negated_conjecture,[],[f12]) ).
thf(f12,conjecture,
! [X6: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
( vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X6)
=> vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X6) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
thf(f147,plain,
~ spl3_2,
inference(avatar_split_clause,[],[f14,f144]) ).
thf(f144,plain,
( spl3_2
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
thf(f14,plain,
$true != $false,
introduced(fool_axiom,[]) ).
thf(f142,plain,
~ spl3_1,
inference(avatar_split_clause,[],[f135,f139]) ).
thf(f135,plain,
vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != sK0,
inference(equality_proxy_clausification,[],[f134]) ).
thf(f134,plain,
$false = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),sK0),
inference(not_proxy_clausification,[],[f63]) ).
thf(f63,plain,
$true = vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),sK0)),
inference(cnf_transformation,[],[f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP019^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 16:17:37 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (12979)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (12980)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (12984)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 % (12983)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (12985)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 % (12981)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 % Exception at run slice level
% 0.14/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs% Exception at run slice level
% 0.14/0.38
% 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 % (12986)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)
% 0.14/0.39 % (12986)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.39 % (12984)First to succeed.
% 0.14/0.39 % (12982)WARNING: value z3 for option sas not known
% 0.14/0.39 % (12982)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 % (12984)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-12979"
% 0.14/0.39 % (12984)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.40 % (12984)------------------------------
% 0.14/0.40 % (12984)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40 % (12984)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (12984)Memory used [KB]: 938
% 0.14/0.40 % (12984)Time elapsed: 0.015 s
% 0.14/0.40 % (12984)Instructions burned: 22 (million)
% 0.14/0.40 % (12979)Success in time 0.02 s
%------------------------------------------------------------------------------