%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU692^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:33:00 AM UTC 2026
% Result : Theorem 0.08s 0.17s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 3
% Syntax : Number of formulae : 61 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 623 ( 176 equ; 0 cnn)
% Maximal formula atoms : 7 ( 10 avg)
% Number of connectives : 1110 ( 17 ~; 55 |; 15 &; 875 @)
% ( 0 <=>; 94 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 22 usr; 9 con; 0-4 aty)
% ( 54 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 191 ( 63 ^; 120 !; 8 ?; 191 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
func: $i > $i > $i > $o ).
thf(func_def_2,type,
funcSet: $i > $i > $i ).
thf(func_def_3,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_4,type,
infuncsetfunc: $o ).
thf(func_def_6,type,
funcext: $o ).
thf(func_def_7,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
vIMP: $o > $o > $o ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_22,type,
vNOT: $o > $o ).
thf(func_def_23,type,
sK4: $i > $i > $i > $i > $i ).
thf(f1,axiom,
( infuncsetfunc
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(f2,axiom,
( funcext
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( func @ X0 @ X1 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(f3,conjecture,
( infuncsetfunc
=> ( funcext
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( funcSet @ X0 @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).
thf(f4,negated_conjecture,
~ ( infuncsetfunc
=> ( funcext
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( funcSet @ X0 @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( infuncsetfunc
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( infuncsetfunc
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( func @ Y2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( funcext
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( func @ X0 @ X1 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( funcext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y2 @ Y1 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( ap @ Y2 @ Y1 @ Y0 @ Y4 )
= ( ap @ Y2 @ Y1 @ Y3 @ Y4 ) ) ) )
=> ( Y0 = Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( infuncsetfunc
=> ( funcext
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( funcSet @ X0 @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( infuncsetfunc = $true )
=> ( ( funcext = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( funcSet @ X0 @ X1 ) )
= $true )
=> ( ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( X2 != X3 )
& ! [X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) )
| ( ( in @ X4 @ X0 )
!= $true ) )
& ( ( in @ X3 @ ( funcSet @ X0 @ X1 ) )
= $true ) )
& ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true ) )
& ( funcext = $true )
& ( infuncsetfunc = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( X2 != X3 )
& ! [X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X4 )
= ( ap @ X0 @ X1 @ X3 @ X4 ) )
| ( ( in @ X4 @ X0 )
!= $true ) )
& ( ( in @ X3 @ ( funcSet @ X0 @ X1 ) )
= $true ) )
& ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true ) )
& ( funcext = $true )
& ( infuncsetfunc = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( sK2 != sK3 )
& ! [X4: $i] :
( ( ( ap @ sK0 @ sK1 @ sK2 @ X4 )
= ( ap @ sK0 @ sK1 @ sK3 @ X4 ) )
| ( $true
!= ( in @ X4 @ sK0 ) ) )
& ( $true
= ( in @ sK3 @ ( funcSet @ sK0 @ sK1 ) ) )
& ( $true
= ( in @ sK2 @ ( funcSet @ sK0 @ sK1 ) ) )
& ( funcext = $true )
& ( infuncsetfunc = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f12]) ).
thf(f14,plain,
( infuncsetfunc
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( func @ Y2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f15,plain,
( funcext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y2 @ Y1 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( ap @ Y2 @ Y1 @ Y0 @ Y4 )
= ( ap @ Y2 @ Y1 @ Y3 @ Y4 ) ) ) )
=> ( Y0 = Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
infuncsetfunc = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
funcext = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
( $true
= ( in @ sK2 @ ( funcSet @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f19,plain,
( $true
= ( in @ sK3 @ ( funcSet @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f20,plain,
! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK0 ) )
| ( ( ap @ sK0 @ sK1 @ sK2 @ X4 )
= ( ap @ sK0 @ sK1 @ sK3 @ X4 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f21,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f13]) ).
thf(f24,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( func @ Y2 @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f14,f16]) ).
thf(f25,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y2 @ Y1 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( ap @ Y2 @ Y1 @ Y0 @ Y4 )
= ( ap @ Y2 @ Y1 @ Y3 @ Y4 ) ) ) )
=> ( Y0 = Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f15,f17]) ).
thf(f26,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y2 @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( func @ Y2 @ Y1 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( ap @ Y2 @ Y1 @ Y0 @ Y4 )
= ( ap @ Y2 @ Y1 @ Y3 @ Y4 ) ) ) )
=> ( Y0 = Y3 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( func @ Y1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y1 @ Y0 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( ap @ Y1 @ Y0 @ X1 @ Y3 )
= ( ap @ Y1 @ Y0 @ Y2 @ Y3 ) ) ) )
=> ( X1 = Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( func @ Y1 @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y1 @ Y0 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( ap @ Y1 @ Y0 @ X1 @ Y3 )
= ( ap @ Y1 @ Y0 @ Y2 @ Y3 ) ) ) )
=> ( X1 = Y2 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( func @ Y0 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( func @ Y0 @ X2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( ap @ Y0 @ X2 @ X1 @ Y2 )
= ( ap @ Y0 @ X2 @ Y1 @ Y2 ) ) ) )
=> ( X1 = Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( func @ Y0 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( func @ Y0 @ X2 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( ap @ Y0 @ X2 @ X1 @ Y2 )
= ( ap @ Y0 @ X2 @ Y1 @ Y2 ) ) ) )
=> ( X1 = Y1 ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( func @ X3 @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( func @ X3 @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ( ap @ X3 @ X2 @ X1 @ Y1 )
= ( ap @ X3 @ X2 @ Y0 @ Y1 ) ) ) )
=> ( X1 = Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( func @ X3 @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ( ap @ X3 @ X2 @ X1 @ Y1 )
= ( ap @ X3 @ X2 @ Y0 @ Y1 ) ) ) )
=> ( X1 = Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( func @ X3 @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ( ap @ X3 @ X2 @ X1 @ Y1 )
= ( ap @ X3 @ X2 @ Y0 @ Y1 ) ) ) )
=> ( X1 = Y0 ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( $true
= ( ( func @ X3 @ X2 @ X4 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( ap @ X3 @ X2 @ X1 @ Y0 )
= ( ap @ X3 @ X2 @ X4 @ Y0 ) ) ) )
=> ( X1 = X4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( $false
= ( func @ X3 @ X2 @ X4 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( ap @ X3 @ X2 @ X1 @ Y0 )
= ( ap @ X3 @ X2 @ X4 @ Y0 ) ) ) )
=> ( X1 = X4 ) ) ) ),
inference(imp_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( $false
= ( func @ X3 @ X2 @ X4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( ap @ X3 @ X2 @ X1 @ Y0 )
= ( ap @ X3 @ X2 @ X4 @ Y0 ) ) ) ) )
| ( $true
= ( X1 = X4 ) ) ),
inference(imp_proxy_clausification,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( $false
= ( func @ X3 @ X2 @ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( ap @ X3 @ X2 @ X1 @ Y0 )
= ( ap @ X3 @ X2 @ X4 @ Y0 ) ) )
@ ( sK4 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $true
= ( X1 = X4 ) ) ),
inference(sigma_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( $false
= ( func @ X3 @ X2 @ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( ap @ X3 @ X2 @ X1 @ Y0 )
= ( ap @ X3 @ X2 @ X4 @ Y0 ) ) )
@ ( sK4 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( X1 = X4 ) ),
inference(equality_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( $false
= ( func @ X3 @ X2 @ X4 ) )
| ( $false
= ( ( in @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) @ X3 )
=> ( ( ap @ X3 @ X2 @ X1 @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) )
= ( ap @ X3 @ X2 @ X4 @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) ) ) ) )
| ( X1 = X4 ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( $false
= ( func @ X3 @ X2 @ X4 ) )
| ( $false
= ( ( ap @ X3 @ X2 @ X1 @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) )
= ( ap @ X3 @ X2 @ X4 @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) ) ) )
| ( X1 = X4 ) ),
inference(imp_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) @ X3 ) )
| ( $false
= ( func @ X3 @ X2 @ X4 ) )
| ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( X1 = X4 ) ),
inference(imp_proxy_clausification,[],[f39]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ap @ X3 @ X2 @ X1 @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) )
!= ( ap @ X3 @ X2 @ X4 @ ( sK4 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( func @ X3 @ X2 @ X4 ) )
| ( $false
= ( func @ X3 @ X2 @ X1 ) )
| ( X1 = X4 ) ),
inference(equality_proxy_clausification,[],[f40]) ).
thf(f43,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( funcSet @ Y2 @ Y1 ) )
=> ( func @ Y2 @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f24]) ).
thf(f44,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( funcSet @ Y1 @ Y0 ) )
=> ( func @ Y1 @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( funcSet @ Y1 @ Y0 ) )
=> ( func @ Y1 @ Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( funcSet @ Y0 @ X2 ) )
=> ( func @ Y0 @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( funcSet @ Y0 @ X2 ) )
=> ( func @ Y0 @ X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( funcSet @ X3 @ X2 ) )
=> ( func @ X3 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( funcSet @ X3 @ X2 ) ) )
| ( $true
= ( func @ X3 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f48]) ).
thf(f52,plain,
( ( $true = $false )
| ( $true
= ( func @ sK0 @ sK1 @ sK2 ) ) ),
inference(constrained_superposition,[],[f18,f49]) ).
thf(f53,plain,
( ( $true = $false )
| ( $true
= ( func @ sK0 @ sK1 @ sK3 ) ) ),
inference(constrained_superposition,[],[f19,f49]) ).
thf(f54,plain,
( $true
= ( func @ sK0 @ sK1 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f53]) ).
thf(f55,plain,
( $true
= ( func @ sK0 @ sK1 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f71,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( ap @ sK0 @ sK1 @ sK2 @ ( sK4 @ sK0 @ X0 @ X1 @ X2 ) )
= ( ap @ sK0 @ sK1 @ sK3 @ ( sK4 @ sK0 @ X0 @ X1 @ X2 ) ) )
| ( $false
= ( func @ sK0 @ X2 @ X1 ) )
| ( $false
= ( func @ sK0 @ X2 @ X0 ) )
| ( X0 = X1 ) ),
inference(constrained_superposition,[],[f20,f41]) ).
thf(f72,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( ap @ sK0 @ sK1 @ sK2 @ ( sK4 @ sK0 @ X0 @ X1 @ X2 ) )
= ( ap @ sK0 @ sK1 @ sK3 @ ( sK4 @ sK0 @ X0 @ X1 @ X2 ) ) )
| ( $false
= ( func @ sK0 @ X2 @ X1 ) )
| ( $false
= ( func @ sK0 @ X2 @ X0 ) )
| ( X0 = X1 ) ),
inference(trivial_inequality_removal,[],[f71]) ).
thf(f84,plain,
! [X0: $i] :
( ( ( ap @ sK0 @ sK1 @ sK2 @ ( sK4 @ sK0 @ X0 @ sK3 @ sK1 ) )
!= ( ap @ sK0 @ sK1 @ X0 @ ( sK4 @ sK0 @ X0 @ sK3 @ sK1 ) ) )
| ( $false
= ( func @ sK0 @ sK1 @ sK3 ) )
| ( $false
= ( func @ sK0 @ sK1 @ X0 ) )
| ( sK3 = X0 )
| ( $false
= ( func @ sK0 @ sK1 @ sK3 ) )
| ( $false
= ( func @ sK0 @ sK1 @ X0 ) )
| ( sK3 = X0 ) ),
inference(constrained_superposition,[],[f42,f72]) ).
thf(f85,plain,
! [X0: $i] :
( ( ( ap @ sK0 @ sK1 @ sK2 @ ( sK4 @ sK0 @ X0 @ sK3 @ sK1 ) )
!= ( ap @ sK0 @ sK1 @ X0 @ ( sK4 @ sK0 @ X0 @ sK3 @ sK1 ) ) )
| ( $false
= ( func @ sK0 @ sK1 @ sK3 ) )
| ( $false
= ( func @ sK0 @ sK1 @ X0 ) )
| ( sK3 = X0 ) ),
inference(duplicate_literal_removal,[],[f84]) ).
thf(f87,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( ap @ sK0 @ sK1 @ sK2 @ ( sK4 @ sK0 @ X0 @ sK3 @ sK1 ) )
!= ( ap @ sK0 @ sK1 @ X0 @ ( sK4 @ sK0 @ X0 @ sK3 @ sK1 ) ) )
| ( $false
= ( func @ sK0 @ sK1 @ X0 ) )
| ( sK3 = X0 ) ),
inference(forward_demodulation,[],[f85,f54]) ).
thf(f88,plain,
! [X0: $i] :
( ( ( ap @ sK0 @ sK1 @ sK2 @ ( sK4 @ sK0 @ X0 @ sK3 @ sK1 ) )
!= ( ap @ sK0 @ sK1 @ X0 @ ( sK4 @ sK0 @ X0 @ sK3 @ sK1 ) ) )
| ( $false
= ( func @ sK0 @ sK1 @ X0 ) )
| ( sK3 = X0 ) ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f91,plain,
( ( $false
= ( func @ sK0 @ sK1 @ sK2 ) )
| ( sK2 = sK3 ) ),
inference(equality_resolution,[],[f88]) ).
thf(f92,plain,
( $false
= ( func @ sK0 @ sK1 @ sK2 ) ),
inference(forward_subsumption_resolution,[],[f91,f21]) ).
thf(f95,plain,
$true = $false,
inference(constrained_superposition,[],[f55,f92]) ).
thf(f96,plain,
$false,
inference(trivial_inequality_removal,[],[f95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU692^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 14:11:06 UTC 2026
% 0.08/0.11 % CPUTime :
% 0.08/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.13 Running first-order model finding
% 0.08/0.13 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % (162762)Will run a generic schedule for satisfiability detection.
% 0.08/0.17 % (162768)% WARNING: option uhcvi not known.
% 0.08/0.17 % (162768)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4061493855:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.17 % (162767)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2061156316_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.17 % (162768)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.17 % (162768)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.17 % Exception at run slice level
% 0.08/0.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.17 % (162768) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-162762-162768"...
% 0.08/0.17 % (162768)...printing done.
% 0.08/0.17 % (162769)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3223865753:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.17 % (162768)Refutation found. Thanks to Tanya!
% 0.08/0.17 % SZS status Theorem for theBenchmark
% 0.08/0.17 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.17 % (162768)------------------------------
% 0.08/0.17 % (162768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.17 % (162768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.17 % (162768)CaDiCaL version: 2.1.3
% 0.08/0.17 % (162768)Termination reason: Refutation
% 0.08/0.17 % (162768)Time elapsed: 0.005 s
% 0.08/0.17 % (162768)Peak memory usage: 12 MB
% 0.08/0.17 % (162768)Instructions burned: 16 (million)
% 0.08/0.17 % (162762)Success in time 0.036 s
% 0.08/0.17 % Vampire exiting
%------------------------------------------------------------------------------