%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU638^2 : 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 : n005.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 08:30:27 AM UTC 2026
% Result : Theorem 0.35s 0.42s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 61 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 490 ( 147 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 524 ( 53 ~; 42 |; 38 &; 361 @)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 25 usr; 12 con; 0-4 aty)
% ( 0 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 175 ( 67 ^; 83 !; 25 ?; 175 :)
% 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,
dsetconstrEL: $o ).
thf(func_def_6,type,
dsetconstrER: $o ).
thf(func_def_7,type,
singleton: $i > $o ).
thf(func_def_8,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_9,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
vAND: $o > $o > $o ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
sK0: $i > $o ).
thf(func_def_20,type,
sK3: $i > $o ).
thf(func_def_24,type,
sK7: $i > $o ).
thf(func_def_25,type,
vNOT: $o > $o ).
thf(f1,axiom,
( dsetconstrEL
= ( ! [X1: $i > $o,X2: $i,X0: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(f2,axiom,
! [X1: $i > $o,X2: $i,X0: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f3,axiom,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( X0
= ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(f4,axiom,
( ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) )
= ex1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(f5,conjecture,
( dsetconstrEL
=> ( dsetconstrER
=> ! [X1: $i > $o,X0: $i] :
( ( ex1 @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E1) ).
thf(f6,negated_conjecture,
~ ( dsetconstrEL
=> ( dsetconstrER
=> ! [X1: $i > $o,X0: $i] :
( ( ex1 @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( X1 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( X0
= ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f8,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( dsetconstrEL
=> ( dsetconstrER
=> ! [X0: $i > $o,X1: $i] :
( ( ex1 @ X1
@ ^ [X2: $i] : ( X0 @ X2 ) )
=> ? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X0 @ X3 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f10,plain,
~ ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ! [X0: $i > $o,X1: $i] :
( ( $true
= ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
=> ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( $true
= ( X0 @ X3 ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) )
= ex1 ),
inference(rectify,[],[f4]) ).
thf(f12,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( X0 @ X1 ) )
= dsetconstrER ),
inference(rectify,[],[f2]) ).
thf(f14,plain,
( ! [X2: $i,X1: $i,X0: $i > $o] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
=> ( $true
= ( X0 @ X1 ) ) )
<=> ( dsetconstrER = $true ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( dsetconstrEL
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( in @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f16,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
=> ( $true
= ( in @ X1 @ X2 ) ) )
<=> ( dsetconstrEL = $true ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
~ ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ! [X0: $i > $o,X1: $i] :
( ( $true
= ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
=> ? [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( $true
= ( X0 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f10]) ).
thf(f18,plain,
( ? [X1: $i,X0: $i > $o] :
( ( $true
= ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
!= ( X0 @ X2 ) ) ) )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f19,plain,
( ( dsetconstrER = $true )
& ? [X1: $i,X0: $i > $o] :
( ( $true
= ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
!= ( X0 @ X2 ) ) ) )
& ( dsetconstrEL = $true ) ),
inference(flattening,[],[f18]) ).
thf(f20,plain,
( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
<=> ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f21,plain,
( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( $true
= ( X0 @ X1 ) ) )
<=> ( dsetconstrER = $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f22,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( $true
= ( X0 @ X1 ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( $true
!= ( X0 @ X1 ) ) ) ) ),
inference(nnf_transformation,[],[f21]) ).
thf(f23,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( $true
= ( X0 @ X1 ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
= ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) )
& ( $true
!= ( X3 @ X4 ) ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f24,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( $true
= ( X0 @ X1 ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ( ( $true
= ( in @ sK1
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ) )
& ( $true
!= ( sK0 @ sK1 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f23]) ).
thf(f25,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
& ( $true
= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) ) ),
inference(nnf_transformation,[],[f20]) ).
thf(f26,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ? [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X5 ) )
& ( $true
= ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f27,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ( ( $true
!= ( in @ sK4 @ sK5 ) )
& ( $true
= ( in @ sK4
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( sK3 @ Y0 ) ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f26]) ).
thf(f28,plain,
( ( dsetconstrER = $true )
& ? [X0: $i,X1: $i > $o] :
( ( $true
= ( ex1 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( X1 @ X2 )
!= $true ) ) )
& ( dsetconstrEL = $true ) ),
inference(rectify,[],[f19]) ).
thf(f29,plain,
( ( dsetconstrER = $true )
& ( $true
= ( ex1 @ sK6
@ ^ [Y0: $i] : ( sK7 @ Y0 ) ) )
& ! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK6 ) )
| ( $true
!= ( sK7 @ X2 ) ) )
& ( dsetconstrEL = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f28]) ).
thf(f30,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f33,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( $true
= ( X0 @ X1 ) )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f34,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f37,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( dsetconstrEL != $true ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f38,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[],[f29]) ).
thf(f39,plain,
! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK6 ) )
| ( $true
!= ( sK7 @ X2 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f40,plain,
( $true
= ( ex1 @ sK6
@ ^ [Y0: $i] : ( sK7 @ Y0 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f41,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f29]) ).
thf(f44,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= Y2 )
& ( in @ Y3 @ Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f30,f34]) ).
thf(f45,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true != $true )
| ( $true
= ( X0 @ X1 ) )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f33,f41]) ).
thf(f48,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(definition_unfolding,[],[f37,f38]) ).
thf(f51,plain,
( $true
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= Y2 )
& ( in @ Y3 @ Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) )
@ sK6
@ ^ [Y0: $i] : ( sK7 @ Y0 ) ) ),
inference(definition_unfolding,[],[f40,f44]) ).
thf(f52,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK6 @ sK7 ) )
& ( in @ Y0 @ ( dsetconstr @ sK6 @ sK7 ) ) ) ) ),
inference(beta-eta_normalization,[],[f51]) ).
thf(f53,plain,
( $true
= ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK6 @ sK7 ) )
& ( in @ Y0 @ ( dsetconstr @ sK6 @ sK7 ) ) )
@ sK8 ) ),
inference(sigma_proxy_clausification,[],[f52]) ).
thf(f54,plain,
( $true
= ( ( ( setadjoin @ sK8 @ emptyset )
= ( dsetconstr @ sK6 @ sK7 ) )
& ( in @ sK8 @ ( dsetconstr @ sK6 @ sK7 ) ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
( $true
= ( in @ sK8 @ ( dsetconstr @ sK6 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f54]) ).
thf(f56,plain,
( $true
= ( ( setadjoin @ sK8 @ emptyset )
= ( dsetconstr @ sK6 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f54]) ).
thf(f57,plain,
( ( dsetconstr @ sK6 @ sK7 )
= ( setadjoin @ sK8 @ emptyset ) ),
inference(equality_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( X0 @ X1 ) )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f59,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
!= ( in @ X1 @ ( dsetconstr @ X2 @ X0 ) ) )
| ( $true
= ( X0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f48]) ).
thf(f61,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
!= ( in @ X1 @ ( dsetconstr @ X2 @ X0 ) ) )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
( $true
= ( in @ sK8 @ ( setadjoin @ sK8 @ emptyset ) ) ),
inference(forward_demodulation,[],[f55,f57]) ).
thf(f63,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ sK8 @ emptyset ) ) )
| ( $true
= ( sK7 @ X0 ) ) ),
inference(constrained_superposition,[],[f59,f57]) ).
thf(f64,plain,
( ( $true != $true )
| ( $true
= ( sK7 @ sK8 ) ) ),
inference(constrained_superposition,[],[f63,f62]) ).
thf(f65,plain,
( $true
= ( sK7 @ sK8 ) ),
inference(trivial_inequality_removal,[],[f64]) ).
thf(f66,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ sK8 @ emptyset ) ) )
| ( $true
= ( in @ X0 @ sK6 ) ) ),
inference(constrained_superposition,[],[f61,f57]) ).
thf(f67,plain,
( ( $true != $true )
| ( $true
= ( in @ sK8 @ sK6 ) ) ),
inference(constrained_superposition,[],[f66,f62]) ).
thf(f68,plain,
( $true
= ( in @ sK8 @ sK6 ) ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f69,plain,
( ( $true != $true )
| ( $true
!= ( sK7 @ sK8 ) ) ),
inference(constrained_superposition,[],[f39,f68]) ).
thf(f70,plain,
( $true
!= ( sK7 @ sK8 ) ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f71,plain,
$false,
inference(forward_subsumption_resolution,[],[f70,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU638^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.29 % Computer : n005.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8046.5625MB
% 0.12/0.29 % OS : Linux 6.8.0-71-generic
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Sep 29 14:00:46 UTC 2026
% 0.29/0.30 % CPUTime :
% 0.29/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.29/0.35 Running higher-order theorem proving
% 0.29/0.37 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
% 0.35/0.42 % (1713410)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.35/0.42 % (1713415)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3098989631:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.35/0.42 % (1713415) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1713410-1713415"...
% 0.35/0.42 % (1713415)...printing done.
% 0.35/0.42 % (1713415)Refutation found. Thanks to Tanya!
% 0.35/0.42 % SZS status Theorem for theBenchmark
% 0.35/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.35/0.42 % (1713415)------------------------------
% 0.35/0.42 % (1713415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.42 % (1713415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.42 % (1713415)CaDiCaL version: 2.1.3
% 0.35/0.42 % (1713415)Termination reason: Refutation
% 0.35/0.42 % (1713415)Time elapsed: 0.005 s
% 0.35/0.42 % (1713415)Peak memory usage: 12 MB
% 0.35/0.42 % (1713415)Instructions burned: 7 (million)
% 0.35/0.42 % (1713410)Success in time 0.038 s
% 0.35/0.42 % Vampire exiting
%------------------------------------------------------------------------------