%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU695^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:33:01 AM UTC 2026
% Result : Theorem 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 7
% Syntax : Number of formulae : 110 ( 52 unt; 0 typ; 2 def)
% Number of atoms : 999 ( 260 equ; 24 cnn)
% Maximal formula atoms : 7 ( 9 avg)
% Number of connectives : 1828 ( 64 ~; 108 |; 20 &;1380 @)
% ( 2 <=>; 155 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 82 ( 82 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 28 usr; 12 con; 0-4 aty)
% ( 99 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 415 ( 0 sgn 191 !; 12 ?; 415 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
kpair: $i > $i > $i ).
thf(func_def_2,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_3,type,
dpsetconstrI: $o ).
thf(func_def_5,type,
func: $i > $i > $i > $o ).
thf(func_def_6,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_7,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_8,type,
lamp: $o ).
thf(func_def_9,type,
funcGraphProp2: $o ).
thf(func_def_10,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
vIMP: $o > $o > $o ).
thf(func_def_12,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_24,type,
sK2: $i > $i ).
thf(func_def_26,type,
vNOT: $o > $o ).
thf(func_def_27,type,
sK4: $i > ( $i > $i ) > $i > $i ).
thf(f1,axiom,
( dpsetconstrI
= ( ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 @ X4 )
=> ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [X5: $i,X6: $i] : ( X2 @ X5 @ X6 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(f2,axiom,
( lam
= ( ^ [X0: $i,X1: $i,X2: $i > $i] :
( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] :
( ( X2 @ X3 )
= X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam) ).
thf(f3,axiom,
( lamp
= ( ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ( func @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamp) ).
thf(f4,axiom,
( funcGraphProp2
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(f5,conjecture,
( dpsetconstrI
=> ( lamp
=> ( funcGraphProp2
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) )
@ X3 )
= ( X2 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta1) ).
thf(f6,negated_conjecture,
~ ( dpsetconstrI
=> ( lamp
=> ( funcGraphProp2
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) )
@ X3 )
= ( X2 @ X3 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( dpsetconstrI
= ( ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 @ X4 )
=> ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [X5: $i,X6: $i] : ( X2 @ X5 @ X6 ) ) ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( dpsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y1 @ Y0 @ Y4 )
=> ( in @ ( kpair @ Y0 @ Y4 )
@ ( dpsetconstr @ Y3 @ Y2
@ ^ [Y5: $i,Y6: $i] : ( Y1 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( lam
= ( ^ [X0: $i,X1: $i,X2: $i > $i] :
( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] :
( ( X2 @ X3 )
= X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( lam
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i] :
( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( lamp
= ( ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ( func @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
( lamp
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( Y0 @ Y3 ) @ Y1 ) ) )
=> ( func @ Y2 @ Y1
@ ( lam @ Y2 @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( funcGraphProp2
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f14,plain,
( funcGraphProp2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
=> ( ( ap @ Y2 @ Y1 @ Y0 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
~ ( dpsetconstrI
=> ( lamp
=> ( funcGraphProp2
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [X5: $i] : ( X2 @ X5 ) )
@ X4 )
= ( X2 @ X4 ) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
~ ( ( dpsetconstrI = $true )
=> ( ( lamp = $true )
=> ( ( funcGraphProp2 = $true )
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ ( X2 @ X3 ) @ X1 )
= $true ) )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( X2 @ X4 )
= ( ap @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ X4 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i,X2: $i > $i] :
( ? [X4: $i] :
( ( ( X2 @ X4 )
!= ( ap @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ X4 ) )
& ( ( in @ X4 @ X0 )
= $true ) )
& ! [X3: $i] :
( ( ( in @ ( X2 @ X3 ) @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
& ( funcGraphProp2 = $true )
& ( lamp = $true )
& ( dpsetconstrI = $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i,X2: $i > $i] :
( ? [X4: $i] :
( ( ( X2 @ X4 )
!= ( ap @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ X4 ) )
& ( ( in @ X4 @ X0 )
= $true ) )
& ! [X3: $i] :
( ( ( in @ ( X2 @ X3 ) @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
& ( funcGraphProp2 = $true )
& ( lamp = $true )
& ( dpsetconstrI = $true ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i,X2: $i > $i] :
( ? [X3: $i] :
( ( ( X2 @ X3 )
!= ( ap @ X0 @ X1
@ ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ X3 ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ! [X4: $i] :
( ( $true
= ( in @ ( X2 @ X4 ) @ X1 ) )
| ( ( in @ X4 @ X0 )
!= $true ) ) )
& ( funcGraphProp2 = $true )
& ( lamp = $true )
& ( dpsetconstrI = $true ) ),
inference(rectify,[],[f18]) ).
thf(f20,plain,
( ( ( sK2 @ sK3 )
!= ( ap @ sK0 @ sK1
@ ( lam @ sK0 @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) )
@ sK3 ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ! [X4: $i] :
( ( $true
= ( in @ ( sK2 @ X4 ) @ sK1 ) )
| ( $true
!= ( in @ X4 @ sK0 ) ) )
& ( funcGraphProp2 = $true )
& ( lamp = $true )
& ( dpsetconstrI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f19]) ).
thf(f21,plain,
( dpsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y1 @ Y0 @ Y4 )
=> ( in @ ( kpair @ Y0 @ Y4 )
@ ( dpsetconstr @ Y3 @ Y2
@ ^ [Y5: $i,Y6: $i] : ( Y1 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f22,plain,
( lam
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i] :
( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f23,plain,
( lamp
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( Y0 @ Y3 ) @ Y1 ) ) )
=> ( func @ Y2 @ Y1
@ ( lam @ Y2 @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f24,plain,
( funcGraphProp2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
=> ( ( ap @ Y2 @ Y1 @ Y0 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f25,plain,
dpsetconstrI = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f26,plain,
lamp = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f27,plain,
funcGraphProp2 = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f28,plain,
! [X4: $i] :
( ( $true
= ( in @ ( sK2 @ X4 ) @ sK1 ) )
| ( $true
!= ( in @ X4 @ sK0 ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f29,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f30,plain,
( ( sK2 @ sK3 )
!= ( ap @ sK0 @ sK1
@ ( lam @ sK0 @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) )
@ sK3 ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f33,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y1 @ Y0 @ Y4 )
=> ( in @ ( kpair @ Y0 @ Y4 )
@ ( dpsetconstr @ Y3 @ Y2
@ ^ [Y5: $i,Y6: $i] : ( Y1 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f21,f25]) ).
thf(f34,plain,
( $true
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( Y0 @ Y3 ) @ Y1 ) ) )
=> ( func @ Y2 @ Y1
@ ( ^ [Y3: $i,Y4: $i,Y5: $i > $i] :
( dpsetconstr @ Y3 @ Y4
@ ^ [Y6: $i,Y7: $i] :
( ( Y5 @ Y6 )
= Y7 ) )
@ Y2
@ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f23,f26,f22]) ).
thf(f35,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
=> ( ( ap @ Y2 @ Y1 @ Y0 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f24,f27]) ).
thf(f36,plain,
( ( sK2 @ sK3 )
!= ( ap @ sK0 @ sK1
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i] :
( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) )
@ sK0
@ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) )
@ sK3 ) ),
inference(definition_unfolding,[],[f30,f22]) ).
thf(f37,plain,
( ( sK2 @ sK3 )
!= ( ap @ sK0 @ sK1
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) )
@ sK3 ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y0 )
=> ( ( ap @ Y2 @ Y1 @ Y0 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f35]) ).
thf(f39,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( func @ Y1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ X1 )
=> ( ( ap @ Y1 @ Y0 @ X1 @ Y2 )
= Y3 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( func @ Y1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ X1 )
=> ( ( ap @ Y1 @ Y0 @ X1 @ Y2 )
= Y3 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( func @ Y0 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
=> ( ( ap @ Y0 @ X2 @ X1 @ Y1 )
= Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( func @ Y0 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X1 )
=> ( ( ap @ Y0 @ X2 @ X1 @ Y1 )
= Y2 ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( func @ X3 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( ( ap @ X3 @ X2 @ X1 @ Y0 )
= Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( ( ap @ X3 @ X2 @ X1 @ Y0 )
= Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X1 )
=> ( ( ap @ X3 @ X2 @ X1 @ Y0 )
= Y1 ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( $true
= ( ( in @ X4 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ X1 )
=> ( ( ap @ X3 @ X2 @ X1 @ X4 )
= Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ X1 )
=> ( ( ap @ X3 @ X2 @ X1 @ X4 )
= Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ X1 )
=> ( ( ap @ X3 @ X2 @ X1 @ X4 )
= Y0 ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f47]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $true
= ( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X1 )
=> ( ( ap @ X3 @ X2 @ X1 @ X4 )
= X5 ) ) ) ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( in @ X5 @ X2 ) )
| ( $true
= ( ( in @ ( kpair @ X4 @ X5 ) @ X1 )
=> ( ( ap @ X3 @ X2 @ X1 @ X4 )
= X5 ) ) ) ),
inference(imp_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( in @ X5 @ X2 ) )
| ( $false
= ( in @ ( kpair @ X4 @ X5 ) @ X1 ) )
| ( $true
= ( ( ap @ X3 @ X2 @ X1 @ X4 )
= X5 ) ) ),
inference(imp_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( in @ X5 @ X2 ) )
| ( $false
= ( in @ ( kpair @ X4 @ X5 ) @ X1 ) )
| ( ( ap @ X3 @ X2 @ X1 @ X4 )
= X5 )
| ( $false
= ( in @ X4 @ X3 ) )
| ( $false
= ( func @ X3 @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X1: $i > $i] :
( $true
= ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
=> ( in @ ( Y0 @ Y3 ) @ Y1 ) ) )
=> ( func @ Y2 @ Y1
@ ( ^ [Y3: $i,Y4: $i,Y5: $i > $i] :
( dpsetconstr @ Y3 @ Y4
@ ^ [Y6: $i,Y7: $i] :
( ( Y5 @ Y6 )
= Y7 ) )
@ Y2
@ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f54,plain,
! [X1: $i > $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ ( X1 @ Y2 ) @ Y0 ) ) )
=> ( func @ Y1 @ Y0
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y2: $i] : ( (=) @ ( X1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
! [X2: $i,X1: $i > $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ ( X1 @ Y2 ) @ Y0 ) ) )
=> ( func @ Y1 @ Y0
@ ( dpsetconstr @ Y1 @ Y0
@ ^ [Y2: $i] : ( (=) @ ( X1 @ Y2 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X2: $i,X1: $i > $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( X1 @ Y1 ) @ X2 ) ) )
=> ( func @ Y0 @ X2
@ ( dpsetconstr @ Y0 @ X2
@ ^ [Y1: $i] : ( (=) @ ( X1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X1: $i > $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ ( X1 @ Y1 ) @ X2 ) ) )
=> ( func @ Y0 @ X2
@ ( dpsetconstr @ Y0 @ X2
@ ^ [Y1: $i] : ( (=) @ ( X1 @ Y1 ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X1: $i > $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( X1 @ Y0 ) @ X2 ) ) )
=> ( func @ X3 @ X2
@ ( dpsetconstr @ X3 @ X2
@ ^ [Y0: $i] : ( (=) @ ( X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X1: $i > $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( X1 @ Y0 ) @ X2 ) ) ) )
| ( $true
= ( func @ X3 @ X2
@ ( dpsetconstr @ X3 @ X2
@ ^ [Y0: $i] : ( (=) @ ( X1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i > $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( in @ ( X1 @ Y0 ) @ X2 ) )
@ ( sK4 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( func @ X3 @ X2
@ ( dpsetconstr @ X3 @ X2
@ ^ [Y0: $i] : ( (=) @ ( X1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i > $i] :
( ( $false
= ( ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( X1 @ ( sK4 @ X3 @ X1 @ X2 ) ) @ X2 ) ) )
| ( $true
= ( func @ X3 @ X2
@ ( dpsetconstr @ X3 @ X2
@ ^ [Y0: $i] : ( (=) @ ( X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i > $i] :
( ( $false
= ( in @ ( X1 @ ( sK4 @ X3 @ X1 @ X2 ) ) @ X2 ) )
| ( $true
= ( func @ X3 @ X2
@ ( dpsetconstr @ X3 @ X2
@ ^ [Y0: $i] : ( (=) @ ( X1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i > $i] :
( ( $true
= ( func @ X3 @ X2
@ ( dpsetconstr @ X3 @ X2
@ ^ [Y0: $i] : ( (=) @ ( X1 @ Y0 ) ) ) ) )
| ( $true
= ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f61]) ).
thf(f64,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y1 @ Y0 @ Y4 )
=> ( in @ ( kpair @ Y0 @ Y4 )
@ ( dpsetconstr @ Y3 @ Y2
@ ^ [Y5: $i,Y6: $i] : ( Y1 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f33]) ).
thf(f65,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ X1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ X1 @ Y3 )
=> ( in @ ( kpair @ X1 @ Y3 ) @ ( dpsetconstr @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X2: $i > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ X1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( Y0 @ X1 @ Y3 )
=> ( in @ ( kpair @ X1 @ Y3 ) @ ( dpsetconstr @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: $i > $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( X2 @ X1 @ Y2 )
=> ( in @ ( kpair @ X1 @ Y2 ) @ ( dpsetconstr @ Y1 @ Y0 @ X2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f68,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( X2 @ X1 @ Y2 )
=> ( in @ ( kpair @ X1 @ Y2 ) @ ( dpsetconstr @ Y1 @ Y0 @ X2 ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ( X2 @ X1 @ Y1 )
=> ( in @ ( kpair @ X1 @ Y1 ) @ ( dpsetconstr @ Y0 @ X3 @ X2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ( X2 @ X1 @ Y1 )
=> ( in @ ( kpair @ X1 @ Y1 ) @ ( dpsetconstr @ Y0 @ X3 @ X2 ) ) ) ) ) )
@ X4 ) ),
inference(pi_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i] :
( $true
= ( ( in @ X1 @ X4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( X2 @ X1 @ Y0 )
=> ( in @ ( kpair @ X1 @ Y0 ) @ ( dpsetconstr @ X4 @ X3 @ X2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f72,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X4 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( X2 @ X1 @ Y0 )
=> ( in @ ( kpair @ X1 @ Y0 ) @ ( dpsetconstr @ X4 @ X3 @ X2 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( in @ X1 @ X4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( X2 @ X1 @ Y0 )
=> ( in @ ( kpair @ X1 @ Y0 ) @ ( dpsetconstr @ X4 @ X3 @ X2 ) ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f72]) ).
thf(f74,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( in @ X1 @ X4 ) )
| ( $true
= ( ( in @ X5 @ X3 )
=> ( ( X2 @ X1 @ X5 )
=> ( in @ ( kpair @ X1 @ X5 ) @ ( dpsetconstr @ X4 @ X3 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f75,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( in @ X1 @ X4 ) )
| ( $false
= ( in @ X5 @ X3 ) )
| ( $true
= ( ( X2 @ X1 @ X5 )
=> ( in @ ( kpair @ X1 @ X5 ) @ ( dpsetconstr @ X4 @ X3 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f74]) ).
thf(f76,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( kpair @ X1 @ X5 ) @ ( dpsetconstr @ X4 @ X3 @ X2 ) ) )
| ( $false
= ( in @ X5 @ X3 ) )
| ( $false
= ( X2 @ X1 @ X5 ) )
| ( $false
= ( in @ X1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f75]) ).
thf(f95,plain,
! [X0: $i] :
( ( ( sK2 @ sK3 )
!= X0 )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ X0 )
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) ) ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( $false
= ( func @ sK0 @ sK1
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) ) ) ) ),
inference(constrained_superposition,[],[f37,f52]) ).
thf(f103,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( sK2 @ sK3 )
!= X0 )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ X0 )
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) ) ) )
| ( $false
= ( func @ sK0 @ sK1
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) ) ) ) ),
inference(forward_demodulation,[],[f95,f29]) ).
thf(f104,plain,
! [X0: $i] :
( ( ( sK2 @ sK3 )
!= X0 )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ X0 )
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) ) ) )
| ( $false
= ( func @ sK0 @ sK1
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) ) ) ) ),
inference(trivial_inequality_removal,[],[f103]) ).
thf(f106,definition,
( spl5_1
<=> ( $false
= ( func @ sK0 @ sK1
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f108,plain,
( ( $false
= ( func @ sK0 @ sK1
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) ) ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f106]) ).
thf(f110,definition,
( spl5_2
<=> ! [X0: $i] :
( ( ( sK2 @ sK3 )
!= X0 )
| ( $false
= ( in @ ( kpair @ sK3 @ X0 )
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) ) ) )
| ( $false
= ( in @ X0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f111,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( kpair @ sK3 @ X0 )
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) ) ) ) )
| ( ( sK2 @ sK3 )
!= X0 )
| ( $false
= ( in @ X0 @ sK1 ) ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f110]) ).
thf(f112,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f104,f110,f106]) ).
thf(f115,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) )
@ sK3
@ X0 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( ( sK2 @ sK3 )
!= X0 )
| ( $false
= ( in @ X0 @ sK1 ) ) )
| ~ spl5_2 ),
inference(constrained_superposition,[],[f76,f111]) ).
thf(f116,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) )
@ sK3
@ X0 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( ( sK2 @ sK3 )
!= X0 ) )
| ~ spl5_2 ),
inference(duplicate_literal_removal,[],[f115]) ).
thf(f117,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( ^ [Y0: $i] : ( (=) @ ( sK2 @ Y0 ) )
@ sK3
@ X0 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( ( sK2 @ sK3 )
!= X0 ) )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f116]) ).
thf(f118,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( $false
= ( ( sK2 @ sK3 )
= X0 ) )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( ( sK2 @ sK3 )
!= X0 ) )
| ~ spl5_2 ),
inference(beta-eta_normalization,[],[f117]) ).
thf(f119,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( ( sK2 @ sK3 )
!= X0 )
| ( ( in @ sK3 @ sK0 )
= $false )
| ( ( sK2 @ sK3 )
!= X0 ) )
| ~ spl5_2 ),
inference(equality_proxy_clausification,[],[f118]) ).
thf(f120,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( ( sK2 @ sK3 )
!= X0 )
| ( ( in @ sK3 @ sK0 )
= $false ) )
| ~ spl5_2 ),
inference(duplicate_literal_removal,[],[f119]) ).
thf(f127,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( ( sK2 @ sK3 )
!= X0 ) )
| ~ spl5_2 ),
inference(forward_demodulation,[],[f120,f29]) ).
thf(f128,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK1 ) )
| ( ( sK2 @ sK3 )
!= X0 ) )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f127]) ).
thf(f133,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
!= ( in @ X0 @ sK0 ) )
| ( ( sK2 @ sK3 )
!= ( sK2 @ X0 ) ) )
| ~ spl5_2 ),
inference(constrained_superposition,[],[f28,f128]) ).
thf(f134,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK0 ) )
| ( ( sK2 @ sK3 )
!= ( sK2 @ X0 ) ) )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f133]) ).
thf(f137,plain,
( ( $true != $true )
| ( ( sK2 @ sK3 )
!= ( sK2 @ sK3 ) )
| ~ spl5_2 ),
inference(constrained_superposition,[],[f134,f29]) ).
thf(f141,plain,
( $false
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f137]) ).
thf(f142,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f141]) ).
thf(f145,plain,
( ( $true = $false )
| ( $true
= ( in
@ ( sK4 @ sK0
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ sK1 )
@ sK0 ) )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f63,f108]) ).
thf(f146,plain,
( ( $true
= ( in
@ ( sK4 @ sK0
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ sK1 )
@ sK0 ) )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f145]) ).
thf(f147,plain,
( ( $true
= ( in @ ( sK4 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ~ spl5_1 ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f160,plain,
( ( $true = $false )
| ( $false
= ( in
@ ( ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ ( sK4 @ sK0
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ sK1 ) )
@ sK1 ) )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f108,f62]) ).
thf(f161,plain,
( ( $false
= ( in
@ ( ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ ( sK4 @ sK0
@ ^ [Y0: $i] :
( sK2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ sK1 ) )
@ sK1 ) )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f160]) ).
thf(f162,plain,
( ( $false
= ( in @ ( sK2 @ ( sK4 @ sK0 @ sK2 @ sK1 ) ) @ sK1 ) )
| ~ spl5_1 ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f179,plain,
( ( $true = $false )
| ( $true
!= ( in @ ( sK4 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f162,f28]) ).
thf(f184,plain,
( ( $true
!= ( in @ ( sK4 @ sK0 @ sK2 @ sK1 ) @ sK0 ) )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f179]) ).
thf(f187,plain,
( $false
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f184,f147]) ).
thf(f188,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f187]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f112]) ).
cnf(s2,plain,
~ spl5_2,
inference(sat_conversion,[],[f142]) ).
cnf(s4,plain,
~ spl5_1,
inference(sat_conversion,[],[f188]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s2,s4]) ).
thf(f189,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU695^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n011.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:11:16 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.29 % (149464)Will run a generic schedule for satisfiability detection.
% 0.19/0.29 % (149471)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=887207819:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.29 % (149470)% WARNING: option uhcvi not known.
% 0.19/0.29 % (149472)dis+10_1_sil=32000:sp=arity:random_seed=944696086:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.29 % (149469)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1638697223_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.29 % (149470)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2336438084:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.29 % (149474)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1825511423:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.29 % (149470)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.29 % Exception at run slice level% (149470)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.29
% 0.19/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.29 % (149473)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2098591030:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.29 % (149473)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.29 % (149475)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=310055722:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.29 % (149481)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1911046871:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.29 % (149473) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-149464-149473"...
% 0.19/0.29 % Exception at run slice level
% 0.19/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.29 % (149473)...printing done.
% 0.19/0.29 % (149473)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Theorem for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (149473)------------------------------
% 0.19/0.29 % (149473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (149473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (149473)CaDiCaL version: 2.1.3
% 0.19/0.29 % (149473)Termination reason: Refutation
% 0.19/0.29 % (149473)Time elapsed: 0.017 s
% 0.19/0.29 % (149473)Peak memory usage: 13 MB
% 0.19/0.29 % (149473)Instructions burned: 31 (million)
% 0.19/0.29 % (149464)Success in time 0.059 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------