%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n015.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 08:32:50 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of formulae : 62 ( 41 unt; 0 typ; 1 def)
% Number of atoms : 471 ( 118 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 669 ( 19 ~; 15 |; 15 &; 558 @)
% ( 1 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 23 ( 19 usr; 12 con; 0-4 aty)
% ( 24 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 92 ( 0 sgn 54 !; 8 ?; 92 :)
% 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_7,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
vIMP: $o > $o > $o ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
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
= ( ! [X0: $i,X1: $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
=> ! [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(f5,negated_conjecture,
~ ( uniqinunit
=> ( secondinupair
=> ( setukpairinjR12
=> ! [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 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( secondinupair
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( secondinupair
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( setukpairinjR12
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f11,plain,
~ ( uniqinunit
=> ( secondinupair
=> ( setukpairinjR12
=> ! [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 ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f12,plain,
~ ( ( uniqinunit = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairinjR12 = $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 ) ) )
=> ( ( X2 = X3 )
=> ( X1 = X3 ) ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 != X3 )
& ( X2 = X3 )
& ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( setukpairinjR12 = $true )
& ( secondinupair = $true )
& ( uniqinunit = $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 != X3 )
& ( X2 = X3 )
& ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( setukpairinjR12 = $true )
& ( secondinupair = $true )
& ( uniqinunit = $true ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( ( sK1 != sK3 )
& ( sK2 = sK3 )
& ( ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) )
& ( setukpairinjR12 = $true )
& ( secondinupair = $true )
& ( uniqinunit = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f14]) ).
thf(f16,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f17,plain,
( secondinupair
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f18,plain,
( setukpairinjR12
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f19,plain,
uniqinunit = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f20,plain,
secondinupair = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f21,plain,
setukpairinjR12 = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f22,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,[],[f15]) ).
thf(f23,plain,
sK2 = sK3,
inference(cnf_transformation,[],[f15]) ).
thf(f24,plain,
sK1 != sK3,
inference(cnf_transformation,[],[f15]) ).
thf(f27,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f16,f19]) ).
thf(f28,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f17,f20]) ).
thf(f29,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ emptyset ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f18,f21]) ).
thf(f30,plain,
( ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ),
inference(definition_unfolding,[],[f22,f23,f23]) ).
thf(f31,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f32,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f31]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ emptyset ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( X2 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( X2 = X1 ) )
| ( $true
= ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
inference(imp_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( ( X1 != X2 )
| ( $true
= ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
inference(equality_proxy_clausification,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) )
| ( X1 != X2 ) ),
inference(equality_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f28]) ).
thf(f39,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f43,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X2 = X1 ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f46]) ).
thf(f61,plain,
( $true
= ( in @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ) ),
inference(constrained_superposition,[],[f41,f30]) ).
thf(f99,plain,
( ( $true
= ( in @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ emptyset ) ) )
| ( sK3 != sK3 ) ),
inference(constrained_superposition,[],[f61,f37]) ).
thf(f102,plain,
( $true
= ( in @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ emptyset ) ) ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f109,definition,
( spl4_6
<=> ( $true
= ( in @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f111,plain,
( ( $true
= ( in @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ emptyset ) ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f109]) ).
thf(f113,plain,
spl4_6,
inference(avatar_split_clause,[],[f102,f109]) ).
thf(f124,plain,
( ( $true = $false )
| ( ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= ( setadjoin @ sK3 @ emptyset ) )
| ~ spl4_6 ),
inference(constrained_superposition,[],[f47,f111]) ).
thf(f125,plain,
( ( ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= ( setadjoin @ sK3 @ emptyset ) )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f124]) ).
thf(f131,plain,
( ( $true
= ( in @ sK1 @ ( setadjoin @ sK3 @ emptyset ) ) )
| ~ spl4_6 ),
inference(constrained_superposition,[],[f41,f125]) ).
thf(f136,plain,
( ( $true = $false )
| ( sK1 = sK3 )
| ~ spl4_6 ),
inference(constrained_superposition,[],[f131,f47]) ).
thf(f139,plain,
( ( sK1 = sK3 )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f136]) ).
thf(f142,plain,
( $false
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f139,f24]) ).
thf(f143,plain,
~ spl4_6,
inference(avatar_contradiction_clause,[],[f142]) ).
cnf(s5,plain,
spl4_6,
inference(sat_conversion,[],[f113]) ).
cnf(s7,plain,
~ spl4_6,
inference(sat_conversion,[],[f143]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s5,s7]) ).
thf(f144,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU651^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 % Computer : n015.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 14:06:03 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.25 Running first-order model finding
% 0.09/0.25 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
% 0.22/0.30 % (3576487)Will run a generic schedule for satisfiability detection.
% 0.22/0.30 % (3576493)% WARNING: option uhcvi not known.
% 0.22/0.30 % (3576493)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1636915867:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.30 % (3576493)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.30 % (3576493)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.30 % (3576493) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3576487-3576493"...
% 0.22/0.30 % (3576493)...printing done.
% 0.22/0.30 % (3576493)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
% 0.22/0.30 % (3576493)------------------------------
% 0.22/0.30 % (3576493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (3576493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (3576493)CaDiCaL version: 2.1.3
% 0.22/0.30 % (3576493)Termination reason: Refutation
% 0.22/0.30 % (3576493)Time elapsed: 0.009 s
% 0.22/0.30 % (3576493)Peak memory usage: 13 MB
% 0.22/0.30 % (3576493)Instructions burned: 15 (million)
% 0.22/0.30 % (3576487)Success in time 0.042 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------