TSTP Solution File: SET593^5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET593^5 : 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 : n025.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 09:14:20 EDT 2024
% Result : Theorem 0.21s 0.38s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 27
% Syntax : Number of formulae : 70 ( 1 unt; 16 typ; 0 def)
% Number of atoms : 725 ( 144 equ; 0 cnn)
% Maximal formula atoms : 14 ( 13 avg)
% Number of connectives : 260 ( 101 ~; 74 |; 56 &; 0 @)
% ( 6 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 87 ( 86 >; 1 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 9 con; 0-6 aty)
% Number of variables : 96 ( 0 ^ 62 !; 28 ?; 96 :)
% ( 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 ) > ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_5,type,
sK1: ( a > $o ) > ( a > $o ) > ( a > $o ) > a ).
thf(func_def_6,type,
sK2: a > $o ).
thf(func_def_7,type,
sK3: a > $o ).
thf(func_def_8,type,
sK4: a > $o ).
thf(func_def_9,type,
sK5: a ).
thf(func_def_11,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_12,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_13,type,
vAND: $o > $o > $o ).
thf(func_def_14,type,
vOR: $o > $o > $o ).
thf(func_def_15,type,
vIMP: $o > $o > $o ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(func_def_17,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f120,plain,
$false,
inference(avatar_sat_refutation,[],[f35,f40,f45,f86,f108,f113,f119]) ).
thf(f119,plain,
( ~ spl6_1
| ~ spl6_5 ),
inference(avatar_contradiction_clause,[],[f118]) ).
thf(f118,plain,
( $false
| ~ spl6_1
| ~ spl6_5 ),
inference(subsumption_resolution,[],[f117,f103]) ).
thf(f103,plain,
( ( $true = vAPP(a,$o,sK4,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,sK2),sK3),sK4)) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f101]) ).
thf(f101,plain,
( spl6_5
<=> ( $true = vAPP(a,$o,sK4,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,sK2),sK3),sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).
thf(f117,plain,
( ( $true != vAPP(a,$o,sK4,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,sK2),sK3),sK4)) )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f114]) ).
thf(f114,plain,
( ( $true != $true )
| ( $true != vAPP(a,$o,sK4,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,sK2),sK3),sK4)) )
| ~ spl6_1 ),
inference(superposition,[],[f22,f30]) ).
thf(f30,plain,
( ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),$o)),sP0,sK2),sK3),sK4) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f28]) ).
thf(f28,plain,
( spl6_1
<=> ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),$o)),sP0,sK2),sK3),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
thf(f22,plain,
! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),$o)),sP0,X2),X1),X0) )
| ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,X2),X1),X0)) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,X2),X1),X0)) )
& ( $true != vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,X2),X1),X0)) )
& ( $true = vAPP(a,$o,X2,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,X2),X1),X0)) ) )
| ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),$o)),sP0,X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f13,f14]) ).
thf(f14,plain,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X3: a] :
( ( vAPP(a,$o,X0,X3) != $true )
& ( vAPP(a,$o,X1,X3) != $true )
& ( vAPP(a,$o,X2,X3) = $true ) )
=> ( ( $true != vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,X2),X1),X0)) )
& ( $true != vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,X2),X1),X0)) )
& ( $true = vAPP(a,$o,X2,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,X2),X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X3: a] :
( ( vAPP(a,$o,X0,X3) != $true )
& ( vAPP(a,$o,X1,X3) != $true )
& ( vAPP(a,$o,X2,X3) = $true ) )
| ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),$o)),sP0,X2),X1),X0) ) ),
inference(rectify,[],[f12]) ).
thf(f12,plain,
! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ? [X5: a] :
( ( $true != vAPP(a,$o,X2,X5) )
& ( $true != vAPP(a,$o,X1,X5) )
& ( $true = vAPP(a,$o,X0,X5) ) )
| ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),$o)),sP0,X0),X1),X2) ) ),
inference(nnf_transformation,[],[f10]) ).
thf(f10,plain,
! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ? [X5: a] :
( ( $true != vAPP(a,$o,X2,X5) )
& ( $true != vAPP(a,$o,X1,X5) )
& ( $true = vAPP(a,$o,X0,X5) ) )
| ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),$o)),sP0,X0),X1),X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f113,plain,
( ~ spl6_6
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f112,f28,f105]) ).
thf(f105,plain,
( spl6_6
<=> ( $true = vAPP(a,$o,sK3,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,sK2),sK3),sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).
thf(f112,plain,
( ( $true != vAPP(a,$o,sK3,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,sK2),sK3),sK4)) )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f109,plain,
( ( $true != $true )
| ( $true != vAPP(a,$o,sK3,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,sK2),sK3),sK4)) )
| ~ spl6_1 ),
inference(superposition,[],[f21,f30]) ).
thf(f21,plain,
! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),$o)),sP0,X2),X1),X0) )
| ( $true != vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,X2),X1),X0)) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f108,plain,
( spl6_5
| spl6_6
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f99,f28,f105,f101]) ).
thf(f99,plain,
( ( $true = vAPP(a,$o,sK3,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,sK2),sK3),sK4)) )
| ( $true = vAPP(a,$o,sK4,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,sK2),sK3),sK4)) )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f98]) ).
thf(f98,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,sK3,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,sK2),sK3),sK4)) )
| ( $true = vAPP(a,$o,sK4,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,sK2),sK3),sK4)) )
| ~ spl6_1 ),
inference(superposition,[],[f23,f97]) ).
thf(f97,plain,
( ( $true = vAPP(a,$o,sK2,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,sK2),sK3),sK4)) )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f94]) ).
thf(f94,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,sK2,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,sK2),sK3),sK4)) )
| ~ spl6_1 ),
inference(superposition,[],[f20,f30]) ).
thf(f20,plain,
! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( $true != vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),$o)),sP0,X2),X1),X0) )
| ( $true = vAPP(a,$o,X2,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),a)),sK1,X2),X1),X0)) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f23,plain,
! [X4: a] :
( ( $true != vAPP(a,$o,sK2,X4) )
| ( $true = vAPP(a,$o,sK3,X4) )
| ( $true = vAPP(a,$o,sK4,X4) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f19,plain,
( ( ( ( $true != vAPP(a,$o,sK3,sK5) )
& ( $true != vAPP(a,$o,sK4,sK5) )
& ( $true = vAPP(a,$o,sK2,sK5) ) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),$o)),sP0,sK2),sK3),sK4) ) )
& ! [X4: a] :
( ( $true = vAPP(a,$o,sK4,X4) )
| ( $true = vAPP(a,$o,sK3,X4) )
| ( $true != vAPP(a,$o,sK2,X4) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f16,f18,f17]) ).
thf(f17,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X3: a] :
( ( vAPP(a,$o,X1,X3) != $true )
& ( vAPP(a,$o,X2,X3) != $true )
& ( vAPP(a,$o,X0,X3) = $true ) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),$o)),sP0,X0),X1),X2) ) )
& ! [X4: a] :
( ( $true = vAPP(a,$o,X2,X4) )
| ( $true = vAPP(a,$o,X1,X4) )
| ( $true != vAPP(a,$o,X0,X4) ) ) )
=> ( ( ? [X3: a] :
( ( $true != vAPP(a,$o,sK3,X3) )
& ( $true != vAPP(a,$o,sK4,X3) )
& ( $true = vAPP(a,$o,sK2,X3) ) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),$o)),sP0,sK2),sK3),sK4) ) )
& ! [X4: a] :
( ( $true = vAPP(a,$o,sK4,X4) )
| ( $true = vAPP(a,$o,sK3,X4) )
| ( $true != vAPP(a,$o,sK2,X4) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f18,plain,
( ? [X3: a] :
( ( $true != vAPP(a,$o,sK3,X3) )
& ( $true != vAPP(a,$o,sK4,X3) )
& ( $true = vAPP(a,$o,sK2,X3) ) )
=> ( ( $true != vAPP(a,$o,sK3,sK5) )
& ( $true != vAPP(a,$o,sK4,sK5) )
& ( $true = vAPP(a,$o,sK2,sK5) ) ) ),
introduced(choice_axiom,[]) ).
thf(f16,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X3: a] :
( ( vAPP(a,$o,X1,X3) != $true )
& ( vAPP(a,$o,X2,X3) != $true )
& ( vAPP(a,$o,X0,X3) = $true ) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),$o)),sP0,X0),X1),X2) ) )
& ! [X4: a] :
( ( $true = vAPP(a,$o,X2,X4) )
| ( $true = vAPP(a,$o,X1,X4) )
| ( $true != vAPP(a,$o,X0,X4) ) ) ),
inference(rectify,[],[f11]) ).
thf(f11,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X4: a] :
( ( $true != vAPP(a,$o,X1,X4) )
& ( $true != vAPP(a,$o,X2,X4) )
& ( $true = vAPP(a,$o,X0,X4) ) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),$o)),sP0,X0),X1),X2) ) )
& ! [X3: a] :
( ( vAPP(a,$o,X2,X3) = $true )
| ( vAPP(a,$o,X1,X3) = $true )
| ( vAPP(a,$o,X0,X3) != $true ) ) ),
inference(definition_folding,[],[f9,f10]) ).
thf(f9,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X4: a] :
( ( $true != vAPP(a,$o,X1,X4) )
& ( $true != vAPP(a,$o,X2,X4) )
& ( $true = vAPP(a,$o,X0,X4) ) )
| ? [X5: a] :
( ( $true != vAPP(a,$o,X2,X5) )
& ( $true != vAPP(a,$o,X1,X5) )
& ( $true = vAPP(a,$o,X0,X5) ) ) )
& ! [X3: a] :
( ( vAPP(a,$o,X2,X3) = $true )
| ( vAPP(a,$o,X1,X3) = $true )
| ( vAPP(a,$o,X0,X3) != $true ) ) ),
inference(flattening,[],[f8]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X4: a] :
( ( $true != vAPP(a,$o,X1,X4) )
& ( $true != vAPP(a,$o,X2,X4) )
& ( $true = vAPP(a,$o,X0,X4) ) )
| ? [X5: a] :
( ( $true != vAPP(a,$o,X2,X5) )
& ( $true != vAPP(a,$o,X1,X5) )
& ( $true = vAPP(a,$o,X0,X5) ) ) )
& ! [X3: a] :
( ( vAPP(a,$o,X2,X3) = $true )
| ( vAPP(a,$o,X1,X3) = $true )
| ( vAPP(a,$o,X0,X3) != $true ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( vAPP(a,$o,X0,X3) = $true )
=> ( ( vAPP(a,$o,X2,X3) = $true )
| ( vAPP(a,$o,X1,X3) = $true ) ) )
=> ( ! [X4: a] :
( ( ( $true != vAPP(a,$o,X2,X4) )
& ( $true = vAPP(a,$o,X0,X4) ) )
=> ( $true = vAPP(a,$o,X1,X4) ) )
& ! [X5: a] :
( ( ( $true != vAPP(a,$o,X1,X5) )
& ( $true = vAPP(a,$o,X0,X5) ) )
=> ( $true = vAPP(a,$o,X2,X5) ) ) ) ),
inference(flattening,[],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( vAPP(a,$o,X0,X3) = $true )
=> ( ( vAPP(a,$o,X2,X3) = $true )
| ( vAPP(a,$o,X1,X3) = $true ) ) )
=> ( ! [X4: a] :
( ( ( $true != vAPP(a,$o,X2,X4) )
& ( $true = vAPP(a,$o,X0,X4) ) )
=> ( $true = vAPP(a,$o,X1,X4) ) )
& ! [X5: a] :
( ( ( $true != vAPP(a,$o,X1,X5) )
& ( $true = vAPP(a,$o,X0,X5) ) )
=> ( $true = vAPP(a,$o,X2,X5) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( vAPP(a,$o,X0,X3)
=> ( vAPP(a,$o,X2,X3)
| vAPP(a,$o,X1,X3) ) )
=> ( ! [X4: a] :
( ( ~ vAPP(a,$o,X2,X4)
& vAPP(a,$o,X0,X4) )
=> vAPP(a,$o,X1,X4) )
& ! [X5: a] :
( ( ~ vAPP(a,$o,X1,X5)
& vAPP(a,$o,X0,X5) )
=> vAPP(a,$o,X2,X5) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( vAPP(a,$o,X0,X3)
=> ( vAPP(a,$o,X2,X3)
| vAPP(a,$o,X1,X3) ) )
=> ( ! [X3: a] :
( ( ~ vAPP(a,$o,X2,X3)
& vAPP(a,$o,X0,X3) )
=> vAPP(a,$o,X1,X3) )
& ! [X3: a] :
( ( ~ vAPP(a,$o,X1,X3)
& vAPP(a,$o,X0,X3) )
=> vAPP(a,$o,X2,X3) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( vAPP(a,$o,X0,X3)
=> ( vAPP(a,$o,X2,X3)
| vAPP(a,$o,X1,X3) ) )
=> ( ! [X3: a] :
( ( ~ vAPP(a,$o,X2,X3)
& vAPP(a,$o,X0,X3) )
=> vAPP(a,$o,X1,X3) )
& ! [X3: a] :
( ( ~ vAPP(a,$o,X1,X3)
& vAPP(a,$o,X0,X3) )
=> vAPP(a,$o,X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_52_pme) ).
thf(f86,plain,
( spl6_2
| spl6_3
| ~ spl6_4 ),
inference(avatar_split_clause,[],[f85,f42,f37,f32]) ).
thf(f32,plain,
( spl6_2
<=> ( $true = vAPP(a,$o,sK3,sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
thf(f37,plain,
( spl6_3
<=> ( $true = vAPP(a,$o,sK4,sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).
thf(f42,plain,
( spl6_4
<=> ( $true = vAPP(a,$o,sK2,sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).
thf(f85,plain,
( ( $true = vAPP(a,$o,sK3,sK5) )
| spl6_3
| ~ spl6_4 ),
inference(subsumption_resolution,[],[f81,f39]) ).
thf(f39,plain,
( ( $true != vAPP(a,$o,sK4,sK5) )
| spl6_3 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f81,plain,
( ( $true = vAPP(a,$o,sK3,sK5) )
| ( $true = vAPP(a,$o,sK4,sK5) )
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f78,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,sK3,sK5) )
| ( $true = vAPP(a,$o,sK4,sK5) )
| ~ spl6_4 ),
inference(superposition,[],[f23,f44]) ).
thf(f44,plain,
( ( $true = vAPP(a,$o,sK2,sK5) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f42]) ).
thf(f45,plain,
( spl6_1
| spl6_4 ),
inference(avatar_split_clause,[],[f24,f42,f28]) ).
thf(f24,plain,
( ( $true = vAPP(a,$o,sK2,sK5) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),$o)),sP0,sK2),sK3),sK4) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f40,plain,
( spl6_1
| ~ spl6_3 ),
inference(avatar_split_clause,[],[f25,f37,f28]) ).
thf(f25,plain,
( ( $true != vAPP(a,$o,sK4,sK5) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),$o)),sP0,sK2),sK3),sK4) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f35,plain,
( spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f26,f32,f28]) ).
thf(f26,plain,
( ( $true != vAPP(a,$o,sK3,sK5) )
| ( $true = vAPP(sTfun(a,$o),$o,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),$o),vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),sTfun(sTfun(a,$o),$o)),sP0,sK2),sK3),sK4) ) ),
inference(cnf_transformation,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET593^5 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n025.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 16:36:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (19235)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.36 % (19239)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.21/0.36 % (19239)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.36 % Exception at run slice level
% 0.21/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.37 % (19236)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.21/0.37 % (19238)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.21/0.37 % (19237)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.37 % (19241)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.21/0.37 % (19242)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.21/0.37 % (19240)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.21/0.37 % (19238)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.37 % Exception at run slice level
% 0.21/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.37 % Exception at run slice level
% 0.21/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.37 % Exception at run slice level
% 0.21/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.37 % (19243)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.37 % Exception at run slice level
% 0.21/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.37 % (19241)First to succeed.
% 0.21/0.38 % (19238)Also succeeded, but the first one will report.
% 0.21/0.38 % (19241)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19235"
% 0.21/0.38 % (19241)Refutation found. Thanks to Tanya!
% 0.21/0.38 % SZS status Theorem for theBenchmark
% 0.21/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38 % (19241)------------------------------
% 0.21/0.38 % (19241)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.38 % (19241)Termination reason: Refutation
% 0.21/0.38
% 0.21/0.38 % (19241)Memory used [KB]: 854
% 0.21/0.38 % (19241)Time elapsed: 0.009 s
% 0.21/0.38 % (19241)Instructions burned: 11 (million)
% 0.21/0.38 % (19235)Success in time 0.022 s
%------------------------------------------------------------------------------