%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU653^2 : 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 : n012.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 08:32:51 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 12
% Syntax : Number of formulae : 128 ( 61 unt; 0 typ; 7 def)
% Number of atoms : 1056 ( 264 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 1728 ( 64 ~; 84 |; 18 &;1411 @)
% ( 7 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 30 usr; 20 con; 0-4 aty)
% ( 71 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 243 ( 0 sgn 151 !; 8 ?; 243 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
secondinupair: $o ).
thf(func_def_5,type,
upairset2E: $o ).
thf(func_def_6,type,
setukpairinjL2: $o ).
thf(func_def_7,type,
setukpairinjR1: $o ).
thf(func_def_8,type,
upairequniteq: $o ).
thf(func_def_9,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
vIMP: $o > $o > $o ).
thf(func_def_14,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vOR: $o > $o > $o ).
thf(func_def_16,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_17,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(f1,axiom,
( secondinupair
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
thf(f2,axiom,
( upairset2E
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X2 = X1 )
| ( X2 = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E) ).
thf(f3,axiom,
( setukpairinjL2
= ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(f4,axiom,
( setukpairinjR1
= ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X2 = X3 )
=> ( X1 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(f6,conjecture,
( secondinupair
=> ( upairset2E
=> ( setukpairinjL2
=> ( setukpairinjR1
=> ( upairequniteq
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X1 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(f7,negated_conjecture,
~ ( secondinupair
=> ( upairset2E
=> ( setukpairinjL2
=> ( setukpairinjR1
=> ( upairequniteq
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X1 = X3 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
( secondinupair
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( secondinupair
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( upairset2E
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X2 = X1 )
| ( X2 = X0 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f11,plain,
( upairset2E
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) )
=> ( ( Y2 = Y0 )
| ( Y1 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( setukpairinjL2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f13,plain,
( setukpairinjR1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( ( Y1 = Y0 )
=> ( Y2 = Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f15,plain,
~ ( secondinupair
=> ( upairset2E
=> ( setukpairinjL2
=> ( setukpairinjR1
=> ( upairequniteq
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X1 = X3 ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f16,plain,
~ ( ( secondinupair = $true )
=> ( ( upairset2E = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X1 = X3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 != X3 )
& ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjL2 = $true )
& ( upairset2E = $true )
& ( secondinupair = $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 != X3 )
& ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjL2 = $true )
& ( upairset2E = $true )
& ( secondinupair = $true ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ( sK1 != sK3 )
& ( ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjL2 = $true )
& ( upairset2E = $true )
& ( secondinupair = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f18]) ).
thf(f20,plain,
( secondinupair
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f21,plain,
( upairset2E
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) )
=> ( ( Y2 = Y0 )
| ( Y1 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f22,plain,
( setukpairinjL2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f23,plain,
( setukpairinjR1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( ( Y1 = Y0 )
=> ( Y2 = Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f25,plain,
secondinupair = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f26,plain,
upairset2E = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f27,plain,
setukpairinjL2 = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f28,plain,
setukpairinjR1 = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f30,plain,
( ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f31,plain,
sK1 != sK3,
inference(cnf_transformation,[],[f19]) ).
thf(f34,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f20,f25]) ).
thf(f35,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) )
=> ( ( Y2 = Y0 )
| ( Y1 = Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f21,f26]) ).
thf(f36,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y3 = Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f22,f27]) ).
thf(f37,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( ( Y1 = Y0 )
=> ( Y2 = Y0 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f23,f28]) ).
thf(f48,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( ( Y1 = Y0 )
=> ( Y2 = Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f37]) ).
thf(f49,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( ( Y0 = X1 )
=> ( Y1 = X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( ( Y0 = X1 )
=> ( Y1 = X1 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X2 = X1 )
=> ( Y0 = X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X2 = X1 )
=> ( Y0 = X1 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X2 = X1 )
=> ( X3 = X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X2 = X1 )
=> ( X3 = X1 ) ) )
@ X4 ) ),
inference(pi_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $true
= ( ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X2 = X1 )
=> ( X3 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
| ( $true
= ( ( X2 = X1 )
=> ( X3 = X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
| ( $true
= ( ( X2 = X1 )
=> ( X3 = X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
| ( $false
= ( X2 = X1 ) )
| ( $true
= ( X3 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
| ( X1 != X2 )
| ( $true
= ( X3 = X1 ) ) ),
inference(equality_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
| ( X1 = X3 )
| ( X1 != X2 ) ),
inference(equality_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y3 = Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f36]) ).
thf(f62,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y2 = Y0 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = X2 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f64]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X2 ) ) ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f67,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X2 ) )
@ X4 ) ),
inference(pi_proxy_clausification,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $true
= ( ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X4 = X2 ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
| ( $true
= ( X4 = X2 ) ) ),
inference(imp_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
| ( $true
= ( X4 = X2 ) ) ),
inference(equality_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
| ( X2 = X4 ) ),
inference(equality_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) )
=> ( ( Y2 = Y0 )
| ( Y1 = Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f35]) ).
thf(f73,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y1 = X1 )
| ( Y0 = X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f74,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( Y1 = X1 )
| ( Y0 = X1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f73]) ).
thf(f75,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ X2 @ emptyset ) ) )
=> ( ( Y0 = X1 )
| ( X2 = X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f76,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ X2 @ emptyset ) ) )
=> ( ( Y0 = X1 )
| ( X2 = X1 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) )
=> ( ( X3 = X1 )
| ( X2 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) )
| ( $true
= ( ( X3 = X1 )
| ( X2 = X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) )
| ( $true
= ( X2 = X1 ) )
| ( $true
= ( X3 = X1 ) ) ),
inference(or_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) )
| ( X1 = X2 )
| ( $true
= ( X3 = X1 ) ) ),
inference(equality_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) )
| ( X1 = X2 )
| ( X1 = X3 ) ),
inference(equality_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f83,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(beta-eta_normalization,[],[f84]) ).
thf(f95,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) )
= X0 )
| ( ( setadjoin @ sK2 @ emptyset )
= X0 ) ),
inference(constrained_superposition,[],[f81,f30]) ).
thf(f107,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
| ( sK2 = X0 ) ),
inference(constrained_superposition,[],[f71,f30]) ).
thf(f112,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
| ( sK3 = X1 )
| ( sK2 != sK3 ) ),
inference(constrained_superposition,[],[f60,f30]) ).
thf(f113,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) @ emptyset ) ) )
| ( ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) )
= X1 )
| ( X0 != X1 ) ),
inference(constrained_superposition,[],[f60,f30]) ).
thf(f117,definition,
( spl4_3
<=> ( sK2 = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f119,plain,
( ( sK2 != sK3 )
| spl4_3 ),
inference(avatar_component_clause,[],[f117]) ).
thf(f121,definition,
( spl4_4
<=> ! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
| ( sK3 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f122,plain,
( ! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
| ( sK3 = X1 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f121]) ).
thf(f123,plain,
( ~ spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f112,f121,f117]) ).
thf(f137,definition,
( spl4_7
<=> ( ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f139,plain,
( ( ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f137]) ).
thf(f142,plain,
( ( $true = $false )
| ( ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ( ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= ( setadjoin @ sK2 @ emptyset ) ) ),
inference(constrained_superposition,[],[f95,f85]) ).
thf(f147,plain,
( ( ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ( ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= ( setadjoin @ sK2 @ emptyset ) ) ),
inference(trivial_inequality_removal,[],[f142]) ).
thf(f149,definition,
( spl4_8
<=> ( ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= ( setadjoin @ sK2 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
thf(f151,plain,
( ( ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= ( setadjoin @ sK2 @ emptyset ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f149]) ).
thf(f153,plain,
( spl4_8
| spl4_7 ),
inference(avatar_split_clause,[],[f147,f137,f149]) ).
thf(f166,plain,
sK0 = sK2,
inference(equality_resolution,[],[f107]) ).
thf(f191,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) @ emptyset ) ) )
| ( ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) )
= X1 )
| ( X0 != X1 ) ),
inference(forward_demodulation,[],[f113,f166]) ).
thf(f192,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) @ emptyset ) ) )
| ( ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) )
= X1 )
| ( X0 != X1 ) ),
inference(forward_demodulation,[],[f191,f166]) ).
thf(f194,plain,
( ( ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ( ( setadjoin @ sK0 @ emptyset )
!= ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) ) ),
inference(equality_resolution,[],[f192]) ).
thf(f196,definition,
( spl4_11
<=> ( ( setadjoin @ sK0 @ emptyset )
= ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
thf(f198,plain,
( ( ( setadjoin @ sK0 @ emptyset )
!= ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) )
| spl4_11 ),
inference(avatar_component_clause,[],[f196]) ).
thf(f200,definition,
( spl4_12
<=> ( ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_12])],[avatar_definition]) ).
thf(f202,plain,
( ( ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ~ spl4_12 ),
inference(avatar_component_clause,[],[f200]) ).
thf(f203,plain,
( ~ spl4_11
| spl4_12 ),
inference(avatar_split_clause,[],[f194,f200,f196]) ).
thf(f204,plain,
( ( ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ~ spl4_7 ),
inference(forward_demodulation,[],[f139,f166]) ).
thf(f205,plain,
( spl4_12
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f204,f137,f200]) ).
thf(f212,plain,
( ( $true
= ( in @ sK3 @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) ) )
| ~ spl4_12 ),
inference(constrained_superposition,[],[f85,f202]) ).
thf(f217,definition,
( spl4_13
<=> ( sK0 = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl4_13])],[avatar_definition]) ).
thf(f219,plain,
( ( sK0 != sK3 )
| spl4_13 ),
inference(avatar_component_clause,[],[f217]) ).
thf(f231,plain,
( ( ( setadjoin @ sK0 @ emptyset )
= ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) )
| ~ spl4_8 ),
inference(forward_demodulation,[],[f151,f166]) ).
thf(f237,plain,
( $false
| ~ spl4_8
| spl4_11 ),
inference(forward_subsumption_resolution,[],[f231,f198]) ).
thf(f238,plain,
( ~ spl4_8
| spl4_11 ),
inference(avatar_contradiction_clause,[],[f237]) ).
thf(f289,plain,
( ( sK0 != sK3 )
| spl4_3 ),
inference(forward_demodulation,[],[f119,f166]) ).
thf(f290,plain,
( ~ spl4_13
| spl4_3 ),
inference(avatar_split_clause,[],[f289,f117,f217]) ).
thf(f292,plain,
( ( sK1 = sK3 )
| ~ spl4_4 ),
inference(equality_resolution,[],[f122]) ).
thf(f293,plain,
( $false
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f292,f31]) ).
thf(f294,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[],[f293]) ).
thf(f303,plain,
( ( $true = $false )
| ( sK1 = sK3 )
| ( sK0 = sK3 )
| ~ spl4_12 ),
inference(constrained_superposition,[],[f212,f81]) ).
thf(f306,plain,
( ( sK1 = sK3 )
| ( sK0 = sK3 )
| ~ spl4_12 ),
inference(trivial_inequality_removal,[],[f303]) ).
thf(f308,plain,
( ( sK0 = sK3 )
| ~ spl4_12 ),
inference(forward_subsumption_resolution,[],[f306,f31]) ).
thf(f311,plain,
( $false
| ~ spl4_12
| spl4_13 ),
inference(forward_subsumption_resolution,[],[f308,f219]) ).
thf(f312,plain,
( ~ spl4_12
| spl4_13 ),
inference(avatar_contradiction_clause,[],[f311]) ).
cnf(s2,plain,
( ~ spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f123]) ).
cnf(s7,plain,
( spl4_7
| spl4_8 ),
inference(sat_conversion,[],[f153]) ).
cnf(s10,plain,
( ~ spl4_11
| spl4_12 ),
inference(sat_conversion,[],[f203]) ).
cnf(s11,plain,
( ~ spl4_7
| spl4_12 ),
inference(sat_conversion,[],[f205]) ).
cnf(s15,plain,
( ~ spl4_8
| spl4_11 ),
inference(sat_conversion,[],[f238]) ).
cnf(s29,plain,
( spl4_3
| ~ spl4_13 ),
inference(sat_conversion,[],[f290]) ).
cnf(s30,plain,
~ spl4_4,
inference(sat_conversion,[],[f294]) ).
cnf(s34,plain,
( ~ spl4_12
| spl4_13 ),
inference(sat_conversion,[],[f312]) ).
cnf(s36,plain,
~ spl4_3,
inference(rat,[],[s2,s30]) ).
cnf(s37,plain,
~ spl4_13,
inference(rat,[],[s29,s36]) ).
cnf(s38,plain,
~ spl4_12,
inference(rat,[],[s34,s37]) ).
cnf(s40,plain,
~ spl4_7,
inference(rat,[],[s11,s38]) ).
cnf(s41,plain,
~ spl4_11,
inference(rat,[],[s10,s38]) ).
cnf(s43,plain,
spl4_8,
inference(rat,[],[s7,s40]) ).
cnf(s45,plain,
$false,
inference(rat,[],[s15,s41,s43]) ).
thf(f313,plain,
$false,
inference(avatar_sat_refutation,[],[s45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU653^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n012.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 14:02:34 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 0.19/0.27 % (151829)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (151835)% WARNING: option uhcvi not known.
% 0.19/0.27 % (151837)dis+10_1_sil=32000:sp=arity:random_seed=331294354:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (151838)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3258877347:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (151834)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2913036081_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.27 % (151836)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=223739016:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (151840)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3925171860:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.27 % (151839)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1880096828:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.27 % (151835)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1413131735:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (151838)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % (151835)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % (151835)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.27 % Exception at run slice level
% 0.19/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.27 % (151837) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-151829-151837"...
% 0.19/0.27 % (151835) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-151829-151835"...
% 0.19/0.27 % (151837)...printing done.
% 0.19/0.27 % (151835)...printing done.
% 0.19/0.27 % (151840) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-151829-151840"...
% 0.19/0.27 % (151838) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-151829-151838"...
% 0.19/0.27 % (151837)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (151837)------------------------------
% 0.19/0.27 % (151837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (151837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (151837)CaDiCaL version: 2.1.3
% 0.19/0.27 % (151837)Termination reason: Refutation
% 0.19/0.27 % (151837)Time elapsed: 0.019 s
% 0.19/0.27 % (151837)Peak memory usage: 12 MB
% 0.19/0.27 % (151837)Instructions burned: 38 (million)
% 0.19/0.27 % (151829)Success in time 0.064 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------