%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU651^2 : 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 : n003.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 08:30:31 AM UTC 2026
% Result : Theorem 0.35s 0.43s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 53 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 545 ( 151 equ; 0 cnn)
% Maximal formula atoms : 6 ( 10 avg)
% Number of connectives : 716 ( 48 ~; 40 |; 35 &; 562 @)
% ( 5 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 16 con; 0-2 aty)
% Number of variables : 98 ( 0 ^; 74 !; 24 ?; 98 :)
% 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,
uniqinunit: $o ).
thf(func_def_5,type,
secondinupair: $o ).
thf(func_def_6,type,
setukpairinjR12: $o ).
thf(func_def_19,type,
vNOT: $o > $o ).
thf(f1,axiom,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(f2,axiom,
( secondinupair
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
thf(f3,axiom,
( setukpairinjR12
= ( ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(f4,conjecture,
( uniqinunit
=> ( secondinupair
=> ( setukpairinjR12
=> ! [X1: $i,X2: $i,X3: $i,X0: $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(f5,negated_conjecture,
~ ( uniqinunit
=> ( secondinupair
=> ( setukpairinjR12
=> ! [X1: $i,X2: $i,X3: $i,X0: $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 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
~ ( uniqinunit
=> ( secondinupair
=> ( setukpairinjR12
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1 = X2 )
=> ( X0 = X2 ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
~ ( ( uniqinunit = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairinjR12 = $true )
=> ! [X3: $i,X1: $i,X0: $i,X2: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1 = X2 )
=> ( X0 = X2 ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( ( uniqinunit = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( setukpairinjR12
= ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f11,plain,
( ( setukpairinjR12 = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( secondinupair
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f13,plain,
( ( secondinupair = $true )
<=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ( setukpairinjR12 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
| ( X0 != X1 ) ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f15,plain,
( ? [X3: $i,X1: $i,X0: $i,X2: $i] :
( ( X0 != X2 )
& ( X1 = X2 )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
& ( setukpairinjR12 = $true )
& ( secondinupair = $true )
& ( uniqinunit = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f16,plain,
( ( setukpairinjR12 = $true )
& ? [X1: $i,X3: $i,X0: $i,X2: $i] :
( ( X0 != X2 )
& ( X1 = X2 )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
& ( uniqinunit = $true )
& ( secondinupair = $true ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) )
<=> ( uniqinunit = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f18,plain,
( ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true ) ) ) ),
inference(nnf_transformation,[],[f17]) ).
thf(f19,plain,
( ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ? [X2: $i,X3: $i] :
( ( X2 != X3 )
& ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= $true ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ( ( sK1 != sK0 )
& ( ( in @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f19]) ).
thf(f21,plain,
( ( setukpairinjR12 = $true )
& ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 != X3 )
& ( X0 = X3 )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( uniqinunit = $true )
& ( secondinupair = $true ) ),
inference(rectify,[],[f16]) ).
thf(f22,plain,
( ( setukpairinjR12 = $true )
& ( sK4 != sK5 )
& ( sK2 = sK5 )
& ( ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK5 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) ) )
& ( uniqinunit = $true )
& ( secondinupair = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f21]) ).
thf(f23,plain,
( ( ( setukpairinjR12 = $true )
| ? [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset )
!= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
& ( X0 = X1 ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
| ( X0 != X1 ) )
| ( setukpairinjR12 != $true ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f24,plain,
( ( ( setukpairinjR12 = $true )
| ? [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset )
!= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
& ( X0 = X1 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ emptyset ) )
| ( X2 != X3 ) )
| ( setukpairinjR12 != $true ) ) ),
inference(rectify,[],[f23]) ).
thf(f25,plain,
( ( ( setukpairinjR12 = $true )
| ( ( ( setadjoin @ ( setadjoin @ sK7 @ emptyset ) @ emptyset )
!= ( setadjoin @ ( setadjoin @ sK7 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK7 @ ( setadjoin @ sK6 @ emptyset ) ) @ emptyset ) ) )
& ( sK7 = sK6 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ emptyset ) )
| ( X2 != X3 ) )
| ( setukpairinjR12 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f24]) ).
thf(f26,plain,
( ( ( secondinupair = $true )
| ? [X1: $i,X0: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true ) )
& ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) ) ),
inference(nnf_transformation,[],[f13]) ).
thf(f27,plain,
( ( ( secondinupair = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) ) ),
inference(rectify,[],[f26]) ).
thf(f28,plain,
( ( ( secondinupair = $true )
| ( ( in @ sK8 @ ( setadjoin @ sK9 @ ( setadjoin @ sK8 @ emptyset ) ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f27]) ).
thf(f31,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( uniqinunit != $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f32,plain,
secondinupair = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f33,plain,
uniqinunit = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f34,plain,
( ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK5 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f35,plain,
sK2 = sK5,
inference(cnf_transformation,[],[f22]) ).
thf(f36,plain,
sK4 != sK5,
inference(cnf_transformation,[],[f22]) ).
thf(f37,plain,
setukpairinjR12 = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f38,plain,
! [X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ emptyset ) )
| ( X2 != X3 )
| ( setukpairinjR12 != $true ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f41,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) )
= $true )
| ( secondinupair != $true ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f45,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( $true != $true )
| ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) ),
inference(definition_unfolding,[],[f31,f33]) ).
thf(f48,plain,
( ( setadjoin @ ( setadjoin @ sK5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK5 @ ( setadjoin @ sK5 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ emptyset ) ) ),
inference(definition_unfolding,[],[f34,f35,f35]) ).
thf(f51,plain,
! [X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ emptyset ) )
| ( X2 != X3 )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f38,f37]) ).
thf(f53,plain,
! [X2: $i,X3: $i] :
( ( $true != $true )
| ( ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) )
= $true ) ),
inference(definition_unfolding,[],[f41,f32]) ).
thf(f54,plain,
! [X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ emptyset )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
| ( $true != $true ) ),
inference(equality_resolution,[],[f51]) ).
thf(f55,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f56,plain,
! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) )
= $true ),
inference(trivial_inequality_removal,[],[f53]) ).
thf(f57,plain,
! [X3: $i] :
( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ emptyset )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f64,plain,
( ( in @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ sK5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK5 @ ( setadjoin @ sK5 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(constrained_superposition,[],[f56,f48]) ).
thf(f65,plain,
( ( in @ ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ sK5 @ emptyset ) @ emptyset ) )
= $true ),
inference(forward_demodulation,[],[f64,f57]) ).
thf(f66,plain,
( ( $true != $true )
| ( ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) )
= ( setadjoin @ sK5 @ emptyset ) ) ),
inference(constrained_superposition,[],[f55,f65]) ).
thf(f67,plain,
( ( setadjoin @ sK3 @ ( setadjoin @ sK4 @ emptyset ) )
= ( setadjoin @ sK5 @ emptyset ) ),
inference(trivial_inequality_removal,[],[f66]) ).
thf(f68,plain,
( ( in @ sK4 @ ( setadjoin @ sK5 @ emptyset ) )
= $true ),
inference(constrained_superposition,[],[f56,f67]) ).
thf(f72,plain,
( ( $true != $true )
| ( sK4 = sK5 ) ),
inference(constrained_superposition,[],[f55,f68]) ).
thf(f73,plain,
sK4 = sK5,
inference(trivial_inequality_removal,[],[f72]) ).
thf(f74,plain,
$false,
inference(forward_subsumption_resolution,[],[f73,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU651^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.29 % Computer : n003.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8046.5625MB
% 0.11/0.29 % OS : Linux 6.8.0-71-generic
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Sep 29 14:04:29 UTC 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.30/0.35 Running higher-order theorem proving
% 0.30/0.37 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
% 0.35/0.43 % (2555648)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.35/0.43 % (2555653)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3112036741:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.35/0.43 % (2555653) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2555648-2555653"...
% 0.35/0.43 % (2555653)...printing done.
% 0.35/0.43 % (2555653)Refutation found. Thanks to Tanya!
% 0.35/0.43 % SZS status Theorem for theBenchmark
% 0.35/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.35/0.43 % (2555653)------------------------------
% 0.35/0.43 % (2555653)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.43 % (2555653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.43 % (2555653)CaDiCaL version: 2.1.3
% 0.35/0.43 % (2555653)Termination reason: Refutation
% 0.35/0.43 % (2555653)Time elapsed: 0.006 s
% 0.35/0.43 % (2555653)Peak memory usage: 12 MB
% 0.35/0.43 % (2555653)Instructions burned: 9 (million)
% 0.35/0.43 % (2555648)Success in time 0.043 s
% 0.35/0.43 % Vampire exiting
%------------------------------------------------------------------------------