TSTP Solution File: SEV120^5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEV120^5 : 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 : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:43:54 EDT 2024
% Result : Theorem 0.17s 0.36s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 28
% Syntax : Number of formulae : 101 ( 6 unt; 21 typ; 0 def)
% Number of atoms : 1476 ( 287 equ; 0 cnn)
% Maximal formula atoms : 30 ( 18 avg)
% Number of connectives : 439 ( 147 ~; 171 |; 88 &; 0 @)
% ( 1 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 149 ( 148 >; 1 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 6 con; 0-6 aty)
% Number of variables : 206 ( 0 ^ 142 !; 58 ?; 206 :)
% ( 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,
sK0: ( a > a > $o ) > $o ).
thf(func_def_5,type,
sK1: a ).
thf(func_def_6,type,
sK2: a ).
thf(func_def_7,type,
sK3: a ).
thf(func_def_8,type,
sK4: a > a > $o ).
thf(func_def_9,type,
sK5: ( a > a > $o ) > a ).
thf(func_def_10,type,
sK6: ( a > a > $o ) > a ).
thf(func_def_11,type,
sK7: ( a > a > $o ) > a ).
thf(func_def_12,type,
sK8: ( a > a > $o ) > a ).
thf(func_def_13,type,
sK9: ( a > a > $o ) > a ).
thf(func_def_14,type,
sK10: ( a > a > $o ) > a ).
thf(func_def_16,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_17,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_18,type,
vAND: $o > $o > $o ).
thf(func_def_19,type,
vOR: $o > $o > $o ).
thf(func_def_20,type,
vIMP: $o > $o > $o ).
thf(func_def_21,type,
vNOT: $o > $o ).
thf(func_def_22,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f688,plain,
$false,
inference(avatar_sat_refutation,[],[f561,f687]) ).
thf(f687,plain,
spl11_4,
inference(avatar_contradiction_clause,[],[f686]) ).
thf(f686,plain,
( $false
| spl11_4 ),
inference(trivial_inequality_removal,[],[f685]) ).
thf(f685,plain,
( ( $true = $false )
| spl11_4 ),
inference(forward_demodulation,[],[f684,f569]) ).
thf(f569,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK2) )
| spl11_4 ),
inference(trivial_inequality_removal,[],[f568]) ).
thf(f568,plain,
( ( $true != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK2) )
| spl11_4 ),
inference(superposition,[],[f377,f4]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f377,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK2) )
| spl11_4 ),
inference(avatar_component_clause,[],[f376]) ).
thf(f376,plain,
( spl11_4
<=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_4])]) ).
thf(f684,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK2) )
| spl11_4 ),
inference(trivial_inequality_removal,[],[f683]) ).
thf(f683,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK2) )
| spl11_4 ),
inference(forward_demodulation,[],[f682,f22]) ).
thf(f22,plain,
$true = vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK3) )
& ( $true = vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
& ! [X5: a,X6: a,X7: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X5),X7) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X6),X7) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X5),X6) ) )
& ! [X8: a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,sK2),sK3) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,X8) )
| ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,vAPP(sTfun(a,sTfun(a,$o)),a,sK5,X8)),vAPP(sTfun(a,sTfun(a,$o)),a,sK7,X8)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,vAPP(sTfun(a,sTfun(a,$o)),a,sK6,X8)),vAPP(sTfun(a,sTfun(a,$o)),a,sK7,X8)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,vAPP(sTfun(a,sTfun(a,$o)),a,sK5,X8)),vAPP(sTfun(a,sTfun(a,$o)),a,sK6,X8)) ) ) )
& ! [X12: a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,sK1),sK2) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,X12) )
| ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,vAPP(sTfun(a,sTfun(a,$o)),a,sK8,X12)),vAPP(sTfun(a,sTfun(a,$o)),a,sK10,X12)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,vAPP(sTfun(a,sTfun(a,$o)),a,sK9,X12)),vAPP(sTfun(a,sTfun(a,$o)),a,sK10,X12)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,vAPP(sTfun(a,sTfun(a,$o)),a,sK8,X12)),vAPP(sTfun(a,sTfun(a,$o)),a,sK9,X12)) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10])],[f9,f13,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: a] :
( ? [X4: a > a > $o] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X1),X3) != $true )
& ( vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X4) = $true )
& ! [X5: a,X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X7) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X6),X7) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X6) != $true ) ) )
& ! [X8: a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X2),X3) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X8) )
| ? [X9: a,X10: a,X11: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X9),X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X10),X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X9),X10) ) ) )
& ! [X12: a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X1),X2) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X12) )
| ? [X13: a,X14: a,X15: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X13),X15) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X14),X15) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X13),X14) ) ) ) )
=> ( ? [X4: a > a > $o] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,sK1),sK3) )
& ( $true = vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,X4) )
& ! [X5: a,X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X7) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X6),X7) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X6) != $true ) ) )
& ! [X8: a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,sK2),sK3) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,X8) )
| ? [X9: a,X10: a,X11: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X9),X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X10),X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X9),X10) ) ) )
& ! [X12: a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,sK1),sK2) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,X12) )
| ? [X13: a,X14: a,X15: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X13),X15) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X14),X15) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X13),X14) ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f11,plain,
( ? [X4: a > a > $o] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,sK1),sK3) )
& ( $true = vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,X4) )
& ! [X5: a,X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X7) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X6),X7) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X6) != $true ) ) )
=> ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK3) )
& ( $true = vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
& ! [X7: a,X6: a,X5: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X5),X7) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X6),X7) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X5),X6) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
! [X8: a > a > $o] :
( ? [X9: a,X10: a,X11: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X9),X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X10),X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X9),X10) ) )
=> ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,vAPP(sTfun(a,sTfun(a,$o)),a,sK5,X8)),vAPP(sTfun(a,sTfun(a,$o)),a,sK7,X8)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,vAPP(sTfun(a,sTfun(a,$o)),a,sK6,X8)),vAPP(sTfun(a,sTfun(a,$o)),a,sK7,X8)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,vAPP(sTfun(a,sTfun(a,$o)),a,sK5,X8)),vAPP(sTfun(a,sTfun(a,$o)),a,sK6,X8)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
! [X12: a > a > $o] :
( ? [X13: a,X14: a,X15: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X13),X15) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X14),X15) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X13),X14) ) )
=> ( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,vAPP(sTfun(a,sTfun(a,$o)),a,sK8,X12)),vAPP(sTfun(a,sTfun(a,$o)),a,sK10,X12)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,vAPP(sTfun(a,sTfun(a,$o)),a,sK9,X12)),vAPP(sTfun(a,sTfun(a,$o)),a,sK10,X12)) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,vAPP(sTfun(a,sTfun(a,$o)),a,sK8,X12)),vAPP(sTfun(a,sTfun(a,$o)),a,sK9,X12)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f9,plain,
? [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: a] :
( ? [X4: a > a > $o] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X1),X3) != $true )
& ( vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X4) = $true )
& ! [X5: a,X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X7) = $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X6),X7) != $true )
| ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X6) != $true ) ) )
& ! [X8: a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X2),X3) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X8) )
| ? [X9: a,X10: a,X11: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X9),X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X10),X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X9),X10) ) ) )
& ! [X12: a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X1),X2) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X12) )
| ? [X13: a,X14: a,X15: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X13),X15) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X14),X15) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X13),X14) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f8,plain,
? [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: a] :
( ? [X12: a > a > $o] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X1),X3) )
& ( $true = vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X12) )
& ! [X13: a,X14: a,X15: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X13),X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X14),X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X13),X14) ) ) )
& ! [X4: a > a > $o] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X2),X3) = $true )
| ( vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X4) != $true )
| ? [X5: a,X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X7) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X6),X7) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X6) = $true ) ) )
& ! [X8: a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X1),X2) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X8) )
| ? [X9: a,X10: a,X11: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X9),X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X10),X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X9),X10) ) ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
? [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: a] :
( ? [X12: a > a > $o] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X1),X3) )
& ( $true = vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X12) )
& ! [X13: a,X14: a,X15: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X13),X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X14),X15) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X13),X14) ) ) )
& ! [X4: a > a > $o] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X2),X3) = $true )
| ( vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X4) != $true )
| ? [X5: a,X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X7) != $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X6),X7) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X6) = $true ) ) )
& ! [X8: a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X1),X2) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X8) )
| ? [X9: a,X10: a,X11: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X9),X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X10),X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X9),X10) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ! [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: a] :
( ( ! [X4: a > a > $o] :
( ( ( vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X4) = $true )
& ! [X5: a,X6: a,X7: a] :
( ( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X6),X7) = $true )
& ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X6) = $true ) )
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X7) = $true ) ) )
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X2),X3) = $true ) )
& ! [X8: a > a > $o] :
( ( ( $true = vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X8) )
& ! [X9: a,X10: a,X11: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X10),X11) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X9),X10) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X9),X11) ) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X1),X2) ) ) )
=> ! [X12: a > a > $o] :
( ( ( $true = vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X12) )
& ! [X13: a,X14: a,X15: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X14),X15) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X13),X14) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X13),X15) ) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X1),X3) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ! [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: a] :
( ( ! [X4: a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X4)
& ! [X5: a,X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X6),X7)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X6) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X7) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X2),X3) )
& ! [X8: a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X8)
& ! [X9: a,X10: a,X11: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X10),X11)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X9),X10) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X9),X11) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,X1),X2) ) )
=> ! [X12: a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X12)
& ! [X13: a,X14: a,X15: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X14),X15)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X13),X14) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X13),X15) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,X1),X3) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: a] :
( ( ! [X4: a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X4)
& ! [X5: a,X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X6),X7)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X6) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X7) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X2),X3) )
& ! [X4: a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X4)
& ! [X5: a,X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X6),X7)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X6) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X7) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X1),X2) ) )
=> ! [X4: a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X4)
& ! [X5: a,X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X6),X7)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X6) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X7) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X1),X3) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: ( a > a > $o ) > $o,X1: a,X2: a,X3: a] :
( ( ! [X4: a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X4)
& ! [X5: a,X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X6),X7)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X6) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X7) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X2),X3) )
& ! [X4: a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X4)
& ! [X5: a,X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X6),X7)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X6) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X7) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X1),X2) ) )
=> ! [X4: a > a > $o] :
( ( vAPP(sTfun(a,sTfun(a,$o)),$o,X0,X4)
& ! [X5: a,X6: a,X7: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X6),X7)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X6) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X5),X7) ) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),X4,X1),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM70_pme) ).
thf(f682,plain,
( ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK2) )
| spl11_4 ),
inference(trivial_inequality_removal,[],[f672]) ).
thf(f672,plain,
( ( $true != $true )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK2) )
| spl11_4 ),
inference(superposition,[],[f663,f15]) ).
thf(f15,plain,
! [X12: a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,vAPP(sTfun(a,sTfun(a,$o)),a,sK8,X12)),vAPP(sTfun(a,sTfun(a,$o)),a,sK9,X12)) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,X12) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,sK1),sK2) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f663,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,vAPP(sTfun(a,sTfun(a,$o)),a,sK8,sK4)),vAPP(sTfun(a,sTfun(a,$o)),a,sK9,sK4)) )
| spl11_4 ),
inference(trivial_inequality_removal,[],[f662]) ).
thf(f662,plain,
( ( $true != $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,vAPP(sTfun(a,sTfun(a,$o)),a,sK8,sK4)),vAPP(sTfun(a,sTfun(a,$o)),a,sK9,sK4)) )
| spl11_4 ),
inference(forward_demodulation,[],[f661,f22]) ).
thf(f661,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,vAPP(sTfun(a,sTfun(a,$o)),a,sK8,sK4)),vAPP(sTfun(a,sTfun(a,$o)),a,sK9,sK4)) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
| spl11_4 ),
inference(trivial_inequality_removal,[],[f660]) ).
thf(f660,plain,
( ( $true = $false )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,vAPP(sTfun(a,sTfun(a,$o)),a,sK8,sK4)),vAPP(sTfun(a,sTfun(a,$o)),a,sK9,sK4)) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
| spl11_4 ),
inference(forward_demodulation,[],[f659,f569]) ).
thf(f659,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,vAPP(sTfun(a,sTfun(a,$o)),a,sK8,sK4)),vAPP(sTfun(a,sTfun(a,$o)),a,sK9,sK4)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK2) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
| spl11_4 ),
inference(trivial_inequality_removal,[],[f626]) ).
thf(f626,plain,
( ( $true = $false )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,vAPP(sTfun(a,sTfun(a,$o)),a,sK8,sK4)),vAPP(sTfun(a,sTfun(a,$o)),a,sK9,sK4)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK2) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
| spl11_4 ),
inference(superposition,[],[f625,f93]) ).
thf(f93,plain,
! [X0: a > a > $o] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,vAPP(sTfun(a,sTfun(a,$o)),a,sK8,X0)),vAPP(sTfun(a,sTfun(a,$o)),a,sK10,X0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,sK1),sK2) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,X0) ) ),
inference(trivial_inequality_removal,[],[f92]) ).
thf(f92,plain,
! [X0: a > a > $o] :
( ( $true != $true )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,sK1),sK2) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,vAPP(sTfun(a,sTfun(a,$o)),a,sK8,X0)),vAPP(sTfun(a,sTfun(a,$o)),a,sK10,X0)) ) ),
inference(superposition,[],[f17,f4]) ).
thf(f17,plain,
! [X12: a > a > $o] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,vAPP(sTfun(a,sTfun(a,$o)),a,sK8,X12)),vAPP(sTfun(a,sTfun(a,$o)),a,sK10,X12)) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,X12) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,sK1),sK2) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f625,plain,
( ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK10,sK4)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK9,sK4)) ) )
| spl11_4 ),
inference(trivial_inequality_removal,[],[f624]) ).
thf(f624,plain,
( ! [X0: a] :
( ( $true = $false )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK10,sK4)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK9,sK4)) ) )
| spl11_4 ),
inference(forward_demodulation,[],[f86,f569]) ).
thf(f86,plain,
! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK10,sK4)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK9,sK4)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK2) ) ),
inference(trivial_inequality_removal,[],[f85]) ).
thf(f85,plain,
! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK10,sK4)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK9,sK4)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK2) ) ),
inference(forward_demodulation,[],[f82,f22]) ).
thf(f82,plain,
! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK10,sK4)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK9,sK4)) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK2) ) ),
inference(trivial_inequality_removal,[],[f81]) ).
thf(f81,plain,
! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK10,sK4)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK9,sK4)) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK2) ) ),
inference(superposition,[],[f21,f16]) ).
thf(f16,plain,
! [X12: a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,vAPP(sTfun(a,sTfun(a,$o)),a,sK9,X12)),vAPP(sTfun(a,sTfun(a,$o)),a,sK10,X12)) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,X12) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X12,sK1),sK2) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
! [X6: a,X7: a,X5: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X6),X7) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X5),X7) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X5),X6) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f561,plain,
~ spl11_4,
inference(avatar_contradiction_clause,[],[f560]) ).
thf(f560,plain,
( $false
| ~ spl11_4 ),
inference(trivial_inequality_removal,[],[f559]) ).
thf(f559,plain,
( ( $true = $false )
| ~ spl11_4 ),
inference(forward_demodulation,[],[f558,f400]) ).
thf(f400,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK2),sK3) )
| ~ spl11_4 ),
inference(trivial_inequality_removal,[],[f389]) ).
thf(f389,plain,
( ( $true = $false )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK2),sK3) )
| ~ spl11_4 ),
inference(superposition,[],[f191,f378]) ).
thf(f378,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK2) )
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f376]) ).
thf(f191,plain,
! [X0: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),sK3) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),X0) ) ),
inference(trivial_inequality_removal,[],[f154]) ).
thf(f154,plain,
! [X0: a] :
( ( $true = $false )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),sK3) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),X0) ) ),
inference(superposition,[],[f53,f117]) ).
thf(f117,plain,
! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),X2) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X1),X2) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f116]) ).
thf(f116,plain,
! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),X2) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X1),X2) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),X1) ) ),
inference(superposition,[],[f59,f4]) ).
thf(f59,plain,
! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X2),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X2),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),X1) ) ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f58,plain,
! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X2),X1) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X2),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),X1) ) ),
inference(superposition,[],[f21,f4]) ).
thf(f53,plain,
$false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK3),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f52,plain,
( ( $true != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK3) ) ),
inference(superposition,[],[f23,f4]) ).
thf(f23,plain,
$true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK1),sK3),
inference(cnf_transformation,[],[f14]) ).
thf(f558,plain,
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK2),sK3) )
| ~ spl11_4 ),
inference(trivial_inequality_removal,[],[f557]) ).
thf(f557,plain,
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK2),sK3) )
| ~ spl11_4 ),
inference(forward_demodulation,[],[f556,f22]) ).
thf(f556,plain,
( ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK2),sK3) )
| ~ spl11_4 ),
inference(trivial_inequality_removal,[],[f546]) ).
thf(f546,plain,
( ( $true != $true )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK2),sK3) )
| ~ spl11_4 ),
inference(superposition,[],[f537,f18]) ).
thf(f18,plain,
! [X8: a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,vAPP(sTfun(a,sTfun(a,$o)),a,sK5,X8)),vAPP(sTfun(a,sTfun(a,$o)),a,sK6,X8)) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,X8) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,sK2),sK3) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f537,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,vAPP(sTfun(a,sTfun(a,$o)),a,sK5,sK4)),vAPP(sTfun(a,sTfun(a,$o)),a,sK6,sK4)) )
| ~ spl11_4 ),
inference(trivial_inequality_removal,[],[f536]) ).
thf(f536,plain,
( ( $true != $true )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,vAPP(sTfun(a,sTfun(a,$o)),a,sK5,sK4)),vAPP(sTfun(a,sTfun(a,$o)),a,sK6,sK4)) )
| ~ spl11_4 ),
inference(forward_demodulation,[],[f535,f22]) ).
thf(f535,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,vAPP(sTfun(a,sTfun(a,$o)),a,sK5,sK4)),vAPP(sTfun(a,sTfun(a,$o)),a,sK6,sK4)) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
| ~ spl11_4 ),
inference(trivial_inequality_removal,[],[f534]) ).
thf(f534,plain,
( ( $true = $false )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,vAPP(sTfun(a,sTfun(a,$o)),a,sK5,sK4)),vAPP(sTfun(a,sTfun(a,$o)),a,sK6,sK4)) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
| ~ spl11_4 ),
inference(forward_demodulation,[],[f533,f400]) ).
thf(f533,plain,
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,vAPP(sTfun(a,sTfun(a,$o)),a,sK5,sK4)),vAPP(sTfun(a,sTfun(a,$o)),a,sK6,sK4)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK2),sK3) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
| ~ spl11_4 ),
inference(trivial_inequality_removal,[],[f504]) ).
thf(f504,plain,
( ( $true = $false )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,vAPP(sTfun(a,sTfun(a,$o)),a,sK5,sK4)),vAPP(sTfun(a,sTfun(a,$o)),a,sK6,sK4)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK2),sK3) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
| ~ spl11_4 ),
inference(superposition,[],[f503,f246]) ).
thf(f246,plain,
! [X0: a > a > $o] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,vAPP(sTfun(a,sTfun(a,$o)),a,sK5,X0)),vAPP(sTfun(a,sTfun(a,$o)),a,sK7,X0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,sK2),sK3) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,X0) ) ),
inference(trivial_inequality_removal,[],[f245]) ).
thf(f245,plain,
! [X0: a > a > $o] :
( ( $true != $true )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,sK2),sK3) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),X0,vAPP(sTfun(a,sTfun(a,$o)),a,sK5,X0)),vAPP(sTfun(a,sTfun(a,$o)),a,sK7,X0)) ) ),
inference(superposition,[],[f20,f4]) ).
thf(f20,plain,
! [X8: a > a > $o] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,vAPP(sTfun(a,sTfun(a,$o)),a,sK5,X8)),vAPP(sTfun(a,sTfun(a,$o)),a,sK7,X8)) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,X8) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,sK2),sK3) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f503,plain,
( ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK7,sK4)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK6,sK4)) ) )
| ~ spl11_4 ),
inference(trivial_inequality_removal,[],[f502]) ).
thf(f502,plain,
( ! [X0: a] :
( ( $true = $false )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK7,sK4)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK6,sK4)) ) )
| ~ spl11_4 ),
inference(forward_demodulation,[],[f138,f400]) ).
thf(f138,plain,
! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK7,sK4)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK6,sK4)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK2),sK3) ) ),
inference(trivial_inequality_removal,[],[f137]) ).
thf(f137,plain,
! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK7,sK4)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK6,sK4)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK2),sK3) ) ),
inference(forward_demodulation,[],[f130,f22]) ).
thf(f130,plain,
! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK7,sK4)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK6,sK4)) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK2),sK3) ) ),
inference(trivial_inequality_removal,[],[f129]) ).
thf(f129,plain,
! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK7,sK4)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,X0),vAPP(sTfun(a,sTfun(a,$o)),a,sK6,sK4)) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,sK4) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),sK4,sK2),sK3) ) ),
inference(superposition,[],[f21,f19]) ).
thf(f19,plain,
! [X8: a > a > $o] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,vAPP(sTfun(a,sTfun(a,$o)),a,sK6,X8)),vAPP(sTfun(a,sTfun(a,$o)),a,sK7,X8)) )
| ( $true != vAPP(sTfun(a,sTfun(a,$o)),$o,sK0,X8) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),X8,sK2),sK3) ) ),
inference(cnf_transformation,[],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV120^5 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n021.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri May 3 12:01:43 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (6136)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.33 % (6140)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.17/0.33 % (6142)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.17/0.33 % (6138)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.17/0.34 % (6137)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.17/0.34 % (6140)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.34 % (6139)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)
% 0.17/0.34 % (6143)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)
% 0.17/0.34 % Exception at run slice level
% 0.17/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.34 % Exception at run slice level
% 0.17/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.34 % (6141)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.17/0.34 % (6139)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.34 % Exception at run slice level
% 0.17/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.34 % Exception at run slice level
% 0.17/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.35 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.17/0.35 % (6144)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)
% 0.17/0.35 % (6145)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:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_476 on theBenchmark for (476ds/0Mi)
% 0.17/0.35 % (6145)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.35 % Exception at run slice level
% 0.17/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.35 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.17/0.35 % (6147)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_396 on theBenchmark for (396ds/0Mi)
% 0.17/0.35 % (6146)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_470 on theBenchmark for (470ds/0Mi)
% 0.17/0.35 % (6146)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.35 % Exception at run slice level
% 0.17/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.36 % (6139)First to succeed.
% 0.17/0.36 % (6139)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-6136"
% 0.17/0.36 % (6139)Refutation found. Thanks to Tanya!
% 0.17/0.36 % SZS status Theorem for theBenchmark
% 0.17/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.36 % (6139)------------------------------
% 0.17/0.36 % (6139)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.17/0.36 % (6139)Termination reason: Refutation
% 0.17/0.36
% 0.17/0.36 % (6139)Memory used [KB]: 958
% 0.17/0.36 % (6139)Time elapsed: 0.025 s
% 0.17/0.36 % (6139)Instructions burned: 54 (million)
% 0.17/0.36 % (6136)Success in time 0.036 s
%------------------------------------------------------------------------------