%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU683^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:30:45 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of formulae : 69 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 500 ( 150 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 554 ( 9 ~; 20 |; 37 &; 393 @)
% ( 0 <=>; 67 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 24 usr; 11 con; 0-4 aty)
% ( 23 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 150 ( 75 ^; 61 !; 14 ?; 150 :)
% 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,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
dsetconstrI: $o ).
thf(func_def_6,type,
uniqinunit: $o ).
thf(func_def_7,type,
singleton: $i > $o ).
thf(func_def_8,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_13,type,
vIMP: $o > $o > $o ).
thf(func_def_14,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_17,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_18,type,
vAND: $o > $o > $o ).
thf(func_def_19,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK1: $i > $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X1: $i > $o,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) )
= dsetconstrI ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(f2,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) )
= uniqinunit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(f3,axiom,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) )
= singleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(f4,axiom,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(f5,conjecture,
( dsetconstrI
=> ( uniqinunit
=> ! [X1: $i > $o,X0: $i] :
( ( ex1 @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E2) ).
thf(f6,negated_conjecture,
~ ( dsetconstrI
=> ( uniqinunit
=> ! [X1: $i > $o,X0: $i] :
( ( ex1 @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) )
= uniqinunit ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
~ ( dsetconstrI
=> ( uniqinunit
=> ! [X0: $i > $o,X1: $i] :
( ( ex1 @ X1
@ ^ [X2: $i] : ( X0 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X0 @ X3 )
=> ( ( X0 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f12,plain,
~ ( ( dsetconstrI = $true )
=> ( ( uniqinunit = $true )
=> ! [X0: $i > $o,X1: $i] :
( ( $true
= ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
=> ( ( $true
= ( X0 @ X3 ) )
=> ( ( $true
= ( X0 @ X4 ) )
=> ( X3 = X4 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( X0
= ( setadjoin @ X1 @ emptyset ) )
& ( in @ X1 @ X0 ) ) )
= singleton ),
inference(rectify,[],[f3]) ).
thf(f14,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ( ( X0 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ) )
= dsetconstrI ),
inference(rectify,[],[f1]) ).
thf(f16,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
~ ( ( dsetconstrI = $true )
=> ( ( uniqinunit = $true )
=> ! [X0: $i > $o,X1: $i] :
( ( $true
= ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( ( $true
= ( X0 @ X2 ) )
=> ( ( $true
= ( X0 @ X3 ) )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f18,plain,
( ? [X0: $i > $o,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( X2 != X3 )
& ( $true
= ( X0 @ X3 ) )
& ( $true
= ( X0 @ X2 ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
& ( $true
= ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( uniqinunit = $true )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f19,plain,
( ( dsetconstrI = $true )
& ( uniqinunit = $true )
& ? [X1: $i,X0: $i > $o] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( $true
= ( X0 @ X3 ) )
& ( $true
= ( X0 @ X2 ) )
& ( X2 != X3 ) ) )
& ( $true
= ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ),
inference(flattening,[],[f18]) ).
thf(f20,plain,
( ( dsetconstrI = $true )
& ( uniqinunit = $true )
& ? [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( X1 @ X3 )
= $true )
& ( ( X1 @ X2 )
= $true )
& ( X2 != X3 ) ) )
& ( $true
= ( ex1 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( dsetconstrI = $true )
& ( uniqinunit = $true )
& ( $true
= ( in @ sK2 @ sK0 ) )
& ( ( in @ sK3 @ sK0 )
= $true )
& ( $true
= ( sK1 @ sK3 ) )
& ( ( sK1 @ sK2 )
= $true )
& ( sK3 != sK2 )
& ( $true
= ( ex1 @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f20]) ).
thf(f22,plain,
( $true
= ( ex1 @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f23,plain,
sK3 != sK2,
inference(cnf_transformation,[],[f21]) ).
thf(f24,plain,
( ( sK1 @ sK2 )
= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f25,plain,
( $true
= ( sK1 @ sK3 ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f26,plain,
( ( in @ sK3 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f27,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f28,plain,
uniqinunit = $true,
inference(cnf_transformation,[],[f21]) ).
thf(f29,plain,
dsetconstrI = $true,
inference(cnf_transformation,[],[f21]) ).
thf(f30,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f31,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f32,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f33,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f36,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ( setadjoin @ Y3 @ emptyset )
= Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f31,f33]) ).
thf(f37,plain,
( $true
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ( setadjoin @ Y3 @ emptyset )
= Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) )
@ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ),
inference(definition_unfolding,[],[f22,f36]) ).
thf(f38,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f30,f28]) ).
thf(f39,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f32,f29]) ).
thf(f40,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) ) ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ( in @ X2 @ X1 )
=> ( ( X3 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( $true
= ( ( X3 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) ) )
| ( $false
= ( in @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( $true
= ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) )
| ( $false
= ( in @ X2 @ X1 ) )
| ( ( X3 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f38]) ).
thf(f49,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y0 = X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X2 = X1 ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f52]) ).
thf(f54,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK0 @ sK1 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK0 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f55,plain,
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK0 @ sK1 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK0 @ sK1 ) ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f54]) ).
thf(f56,plain,
( $true
= ( ( in @ sK4 @ ( dsetconstr @ sK0 @ sK1 ) )
& ( ( setadjoin @ sK4 @ emptyset )
= ( dsetconstr @ sK0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
( ( ( setadjoin @ sK4 @ emptyset )
= ( dsetconstr @ sK0 @ sK1 ) )
= $true ),
inference(and_proxy_clausification,[],[f56]) ).
thf(f59,plain,
( ( dsetconstr @ sK0 @ sK1 )
= ( setadjoin @ sK4 @ emptyset ) ),
inference(equality_proxy_clausification,[],[f57]) ).
thf(f61,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ sK4 @ emptyset ) ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( sK1 @ X0 )
= $false ) ),
inference(constrained_superposition,[],[f47,f59]) ).
thf(f67,plain,
! [X0: $i] :
( ( sK4 = X0 )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $true = $false )
| ( ( sK1 @ X0 )
= $false ) ),
inference(constrained_superposition,[],[f53,f61]) ).
thf(f68,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ sK0 ) )
| ( ( sK1 @ X0 )
= $false )
| ( sK4 = X0 ) ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f70,plain,
( ( sK3 = sK4 )
| ( ( sK1 @ sK3 )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f68,f26]) ).
thf(f71,plain,
( ( $true = $false )
| ( sK2 = sK4 )
| ( ( sK1 @ sK2 )
= $false ) ),
inference(constrained_superposition,[],[f68,f27]) ).
thf(f74,plain,
( ( sK3 = sK4 )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f75,plain,
( ( sK2 = sK4 )
| ( ( sK1 @ sK2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f71]) ).
thf(f78,plain,
( ( sK3 = sK4 )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f74,f25]) ).
thf(f79,plain,
sK3 = sK4,
inference(trivial_inequality_removal,[],[f78]) ).
thf(f80,plain,
( ( $true = $false )
| ( sK2 = sK4 ) ),
inference(forward_demodulation,[],[f75,f24]) ).
thf(f81,plain,
sK2 = sK4,
inference(trivial_inequality_removal,[],[f80]) ).
thf(f92,plain,
sK3 = sK2,
inference(constrained_superposition,[],[f79,f81]) ).
thf(f96,plain,
$false,
inference(forward_subsumption_resolution,[],[f92,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU683^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n006.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:08:10 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.30 % (774841)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (774851)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3933999966:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (774848)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1661700266:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (774846)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=795996220:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (774847)lrs+10_16_si=on:nwc=1.5:random_seed=307354784:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (774850)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2411090117:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (774849)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1057304830:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.30 % (774848)Instruction limit reached!
% 0.22/0.30 % (774848)------------------------------
% 0.22/0.30 % (774848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (774848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (774848)CaDiCaL version: 2.1.3
% 0.22/0.30 % (774848)Termination reason: Instruction limit
% 0.22/0.30 % (774848)Termination phase: Saturation
% 0.22/0.30 % (774848)Time elapsed: 0.002 s
% 0.22/0.30 % (774848)Peak memory usage: 12 MB
% 0.22/0.30 % (774848)Instructions burned: 3 (million)
% 0.22/0.30 % (774847) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-774841-774847"...
% 0.22/0.30 % (774846) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-774841-774846"...
% 0.22/0.30 % (774851) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-774841-774851"...
% 0.22/0.30 % (774847)...printing done.
% 0.22/0.30 % (774846)...printing done.
% 0.22/0.30 % (774847)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.31 % (774847)------------------------------
% 0.22/0.31 % (774847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (774847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (774847)CaDiCaL version: 2.1.3
% 0.22/0.31 % (774847)Termination reason: Refutation
% 0.22/0.31 % (774847)Time elapsed: 0.006 s
% 0.22/0.31 % (774847)Peak memory usage: 12 MB
% 0.22/0.31 % (774847)Instructions burned: 10 (million)
% 0.22/0.31 % (774841)Success in time 0.045 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------