%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV221^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 08:39:10 AM UTC 2026
% Result : Theorem 0.24s 0.31s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of formulae : 112 ( 7 unt; 0 typ; 8 def)
% Number of atoms : 693 ( 175 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 684 ( 190 ~; 208 |; 65 &; 208 @)
% ( 12 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 11 con; 0-4 aty)
% Number of variables : 91 ( 0 sgn 40 !; 28 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cZ: a > $o ).
thf(func_def_1,type,
cW: ( a > $o ) > $o ).
thf(func_def_5,type,
vAND: $o > $o > $o ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_8,type,
sK0: a ).
thf(func_def_9,type,
sK1: a > $o ).
thf(func_def_10,type,
sK2: a > $o ).
thf(func_def_11,type,
sK3: a > $o ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(func_def_14,type,
db1:
!>[X0: $tType] : X0 ).
thf(f1,conjecture,
! [X0: a] :
( ( ( cZ @ X0 )
& ? [X1: a > $o] :
( ( X1 @ X0 )
& ( cW @ X1 ) ) )
<=> ? [X1: a > $o] :
( ( X1 @ X0 )
& ? [X2: a > $o] :
( ( X1
= ( ^ [X3: a] :
( ( X2 @ X3 )
& ( cZ @ X3 ) ) ) )
& ( cW @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM61_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ( ( cZ @ X0 )
& ? [X1: a > $o] :
( ( X1 @ X0 )
& ( cW @ X1 ) ) )
<=> ? [X1: a > $o] :
( ( X1 @ X0 )
& ? [X2: a > $o] :
( ( X1
= ( ^ [X3: a] :
( ( X2 @ X3 )
& ( cZ @ X3 ) ) ) )
& ( cW @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a] :
( ( ( cZ @ X0 )
& ? [X1: a > $o] :
( ( X1 @ X0 )
& ( cW @ X1 ) ) )
<=> ? [X2: a > $o] :
( ( X2 @ X0 )
& ? [X3: a > $o] :
( ( X2
= ( ^ [X4: a] :
( ( X3 @ X4 )
& ( cZ @ X4 ) ) ) )
& ( cW @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a] :
( ( ( ( cZ @ X0 )
= $true )
& ? [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
& ( ( cW @ X1 )
= $true ) ) )
<=> ? [X2: a > $o] :
( ( ( X2 @ X0 )
= $true )
& ? [X3: a > $o] :
( ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) ) )
= X2 )
& ( ( cW @ X3 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a] :
( ( ( ( cZ @ X0 )
= $true )
& ? [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
& ( ( cW @ X1 )
= $true ) ) )
<~> ? [X2: a > $o] :
( ( ( X2 @ X0 )
= $true )
& ? [X3: a > $o] :
( ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) ) )
= X2 )
& ( ( cW @ X3 )
= $true ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a] :
( ( ! [X2: a > $o] :
( ( ( X2 @ X0 )
!= $true )
| ! [X3: a > $o] :
( ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) ) )
!= X2 )
| ( ( cW @ X3 )
!= $true ) ) )
| ( ( cZ @ X0 )
!= $true )
| ! [X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
| ( ( cW @ X1 )
!= $true ) ) )
& ( ? [X2: a > $o] :
( ( ( X2 @ X0 )
= $true )
& ? [X3: a > $o] :
( ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) ) )
= X2 )
& ( ( cW @ X3 )
= $true ) ) )
| ( ( ( cZ @ X0 )
= $true )
& ? [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
& ( ( cW @ X1 )
= $true ) ) ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a] :
( ( ! [X2: a > $o] :
( ( ( X2 @ X0 )
!= $true )
| ! [X3: a > $o] :
( ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) ) )
!= X2 )
| ( ( cW @ X3 )
!= $true ) ) )
| ( ( cZ @ X0 )
!= $true )
| ! [X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
| ( ( cW @ X1 )
!= $true ) ) )
& ( ? [X2: a > $o] :
( ( ( X2 @ X0 )
= $true )
& ? [X3: a > $o] :
( ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X3 @ Y0 ) ) )
= X2 )
& ( ( cW @ X3 )
= $true ) ) )
| ( ( ( cZ @ X0 )
= $true )
& ? [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
& ( ( cW @ X1 )
= $true ) ) ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
? [X0: a] :
( ( ! [X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
| ! [X2: a > $o] :
( ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X2 @ Y0 ) ) )
!= X1 )
| ( ( cW @ X2 )
!= $true ) ) )
| ( ( cZ @ X0 )
!= $true )
| ! [X3: a > $o] :
( ( $true
!= ( X3 @ X0 ) )
| ( ( cW @ X3 )
!= $true ) ) )
& ( ? [X4: a > $o] :
( ( $true
= ( X4 @ X0 ) )
& ? [X5: a > $o] :
( ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X5 @ Y0 ) ) )
= X4 )
& ( $true
= ( cW @ X5 ) ) ) )
| ( ( ( cZ @ X0 )
= $true )
& ? [X6: a > $o] :
( ( $true
= ( X6 @ X0 ) )
& ( $true
= ( cW @ X6 ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( ! [X1: a > $o] :
( ( $true
!= ( X1 @ sK0 ) )
| ! [X2: a > $o] :
( ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X2 @ Y0 ) ) )
!= X1 )
| ( ( cW @ X2 )
!= $true ) ) )
| ( $true
!= ( cZ @ sK0 ) )
| ! [X3: a > $o] :
( ( $true
!= ( X3 @ sK0 ) )
| ( ( cW @ X3 )
!= $true ) ) )
& ( ( ( $true
= ( sK1 @ sK0 ) )
& ( sK1
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK2 @ Y0 ) ) ) )
& ( $true
= ( cW @ sK2 ) ) )
| ( ( $true
= ( cZ @ sK0 ) )
& ( $true
= ( sK3 @ sK0 ) )
& ( $true
= ( cW @ sK3 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X4,sK1),skolemize(X5,sK2),skolemize(X6,sK3)],[f8]) ).
thf(f10,plain,
( ( $true
= ( cW @ sK2 ) )
| ( $true
= ( cW @ sK3 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( ( $true
= ( cW @ sK2 ) )
| ( $true
= ( sK3 @ sK0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( ( sK1
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ( $true
= ( cW @ sK3 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
( ( sK1
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ( $true
= ( sK3 @ sK0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
( ( sK1
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ( $true
= ( cZ @ sK0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
( ( $true
= ( sK1 @ sK0 ) )
| ( $true
= ( cW @ sK3 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f17,plain,
( ( $true
= ( sK1 @ sK0 ) )
| ( $true
= ( sK3 @ sK0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f18,plain,
( ( $true
= ( sK1 @ sK0 ) )
| ( $true
= ( cZ @ sK0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f19,plain,
! [X2: a > $o,X3: a > $o,X1: a > $o] :
( ( $true
!= ( X1 @ sK0 ) )
| ( ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X2 @ Y0 ) ) )
!= X1 )
| ( ( cW @ X2 )
!= $true )
| ( $true
!= ( cZ @ sK0 ) )
| ( $true
!= ( X3 @ sK0 ) )
| ( ( cW @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f22,plain,
! [X2: a > $o,X3: a > $o] :
( ( $true
!= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( X2 @ Y0 ) )
@ sK0 ) )
| ( ( cW @ X2 )
!= $true )
| ( $true
!= ( cZ @ sK0 ) )
| ( $true
!= ( X3 @ sK0 ) )
| ( ( cW @ X3 )
!= $true ) ),
inference(equality_resolution,[],[f19]) ).
thf(f23,plain,
! [X2: a > $o,X3: a > $o] :
( ( $true
!= ( ( cZ @ sK0 )
& ( X2 @ sK0 ) ) )
| ( ( cW @ X2 )
!= $true )
| ( $true
!= ( cZ @ sK0 ) )
| ( $true
!= ( X3 @ sK0 ) )
| ( ( cW @ X3 )
!= $true ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
! [X2: a > $o,X3: a > $o] :
( ( $false
= ( X2 @ sK0 ) )
| ( ( cW @ X2 )
!= $true )
| ( $true
!= ( cZ @ sK0 ) )
| ( $true
!= ( X3 @ sK0 ) )
| ( ( cW @ X3 )
!= $true )
| ( ( cZ @ sK0 )
= $false ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f26,definition,
( spl4_1
<=> ( $true
= ( sK3 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f27,plain,
( ( $true
!= ( sK3 @ sK0 ) )
| spl4_1 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f28,plain,
( ( $true
= ( sK3 @ sK0 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f30,definition,
( spl4_2
<=> ( $true
= ( sK1 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f31,plain,
( ( $true
!= ( sK1 @ sK0 ) )
| spl4_2 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f32,plain,
( ( $true
= ( sK1 @ sK0 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f33,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f17,f30,f26]) ).
thf(f35,definition,
( spl4_3
<=> ( $true
= ( cZ @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f36,plain,
( ( $true
!= ( cZ @ sK0 ) )
| spl4_3 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f37,plain,
( ( $true
= ( cZ @ sK0 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f38,plain,
( spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f18,f30,f35]) ).
thf(f40,definition,
( spl4_4
<=> ( $true
= ( cW @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f42,plain,
( ( $true
= ( cW @ sK2 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f45,definition,
( spl4_5
<=> ( $true
= ( cW @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f46,plain,
( ( $true
!= ( cW @ sK3 ) )
| spl4_5 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f47,plain,
( ( $true
= ( cW @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f48,plain,
( spl4_5
| spl4_4 ),
inference(avatar_split_clause,[],[f10,f40,f45]) ).
thf(f50,definition,
( spl4_6
<=> ( sK1
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f52,plain,
( ( sK1
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f53,plain,
( spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f13,f50,f45]) ).
thf(f54,plain,
( ! [X2: a > $o,X3: a > $o] :
( ( $false
= ( X2 @ sK0 ) )
| ( ( cW @ X2 )
!= $true )
| ( $true
!= ( X3 @ sK0 ) )
| ( ( cW @ X3 )
!= $true )
| ( ( cZ @ sK0 )
= $false ) )
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f24,f37]) ).
thf(f55,plain,
( ! [X2: a > $o,X3: a > $o] :
( ( $true = $false )
| ( $false
= ( X2 @ sK0 ) )
| ( ( cW @ X2 )
!= $true )
| ( $true
!= ( X3 @ sK0 ) )
| ( ( cW @ X3 )
!= $true ) )
| ~ spl4_3 ),
inference(forward_demodulation,[],[f54,f37]) ).
thf(f56,plain,
( ! [X2: a > $o,X3: a > $o] :
( ( $false
= ( X2 @ sK0 ) )
| ( ( cW @ X2 )
!= $true )
| ( $true
!= ( X3 @ sK0 ) )
| ( ( cW @ X3 )
!= $true ) )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f55]) ).
thf(f64,definition,
( spl4_9
<=> ! [X3: a > $o] :
( ( $true
!= ( X3 @ sK0 ) )
| ( ( cW @ X3 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
thf(f65,plain,
( ! [X3: a > $o] :
( ( ( cW @ X3 )
!= $true )
| ( $true
!= ( X3 @ sK0 ) ) )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f64]) ).
thf(f70,definition,
( spl4_11
<=> ! [X2: a > $o] :
( ( $false
= ( X2 @ sK0 ) )
| ( ( cW @ X2 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
thf(f71,plain,
( ! [X2: a > $o] :
( ( ( cW @ X2 )
!= $true )
| ( $false
= ( X2 @ sK0 ) ) )
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f72,plain,
( spl4_9
| spl4_11
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f56,f35,f70,f64]) ).
thf(f114,plain,
( ( $true != $true )
| ( $true
!= ( sK3 @ sK0 ) )
| ~ spl4_5
| ~ spl4_9 ),
inference(constrained_superposition,[],[f65,f47]) ).
thf(f115,plain,
( ( $true
!= ( sK3 @ sK0 ) )
| ~ spl4_5
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f114]) ).
thf(f116,plain,
( $false
| ~ spl4_1
| ~ spl4_5
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f115,f28]) ).
thf(f117,plain,
( ~ spl4_1
| ~ spl4_5
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f116]) ).
thf(f173,plain,
( ( $true != $true )
| ( ( sK3 @ sK0 )
= $false )
| ~ spl4_5
| ~ spl4_11 ),
inference(constrained_superposition,[],[f71,f47]) ).
thf(f174,plain,
( ( ( sK3 @ sK0 )
= $false )
| ~ spl4_5
| ~ spl4_11 ),
inference(trivial_inequality_removal,[],[f173]) ).
thf(f175,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_5
| ~ spl4_11 ),
inference(constrained_superposition,[],[f174,f28]) ).
thf(f179,plain,
( $false
| ~ spl4_1
| ~ spl4_5
| ~ spl4_11 ),
inference(trivial_inequality_removal,[],[f175]) ).
thf(f180,plain,
( ~ spl4_1
| ~ spl4_5
| ~ spl4_11 ),
inference(avatar_contradiction_clause,[],[f179]) ).
thf(f189,plain,
( ( $true
= ( cW @ sK2 ) )
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f11,f27]) ).
thf(f190,plain,
( spl4_4
| spl4_1 ),
inference(avatar_split_clause,[],[f189,f26,f40]) ).
thf(f191,plain,
( spl4_1
| spl4_6 ),
inference(avatar_split_clause,[],[f14,f50,f26]) ).
thf(f192,plain,
( ( sK1
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK2 @ Y0 ) ) ) )
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f15,f36]) ).
thf(f193,plain,
( spl4_6
| spl4_3 ),
inference(avatar_split_clause,[],[f192,f35,f50]) ).
thf(f194,plain,
( ! [X1: a] :
( ( sK1 @ X1 )
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK2 @ Y0 ) )
@ X1 ) )
| ~ spl4_6 ),
inference(argument_congruence,[],[f52]) ).
thf(f196,plain,
( ! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( ^ [Y0: a] :
( ( cZ @ Y0 )
& ( sK2 @ Y0 ) )
@ X1 ) ) )
| ~ spl4_6 ),
inference(iff_proxy_clausification,[],[f194]) ).
thf(f197,plain,
( ! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( ( cZ @ X1 )
& ( sK2 @ X1 ) ) ) )
| ~ spl4_6 ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f198,plain,
( ! [X1: a] :
( ( $true
= ( sK2 @ X1 ) )
| ( $false
= ( sK1 @ X1 ) ) )
| ~ spl4_6 ),
inference(and_proxy_clausification,[],[f197]) ).
thf(f199,plain,
( ! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( cZ @ X1 ) ) )
| ~ spl4_6 ),
inference(and_proxy_clausification,[],[f197]) ).
thf(f217,plain,
( ( $true = $false )
| ( $true
= ( cZ @ sK0 ) )
| ~ spl4_2
| ~ spl4_6 ),
inference(constrained_superposition,[],[f199,f32]) ).
thf(f220,plain,
( ( $true
= ( cZ @ sK0 ) )
| ~ spl4_2
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f217]) ).
thf(f223,plain,
( $false
| ~ spl4_2
| spl4_3
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f220,f36]) ).
thf(f224,plain,
( ~ spl4_2
| spl4_3
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f223]) ).
thf(f226,plain,
( ( $true != $true )
| ( $true
!= ( sK2 @ sK0 ) )
| ~ spl4_4
| ~ spl4_9 ),
inference(constrained_superposition,[],[f65,f42]) ).
thf(f227,plain,
( ( $true
!= ( sK2 @ sK0 ) )
| ~ spl4_4
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f226]) ).
thf(f231,plain,
( ( $true != $true )
| ( ( sK1 @ sK0 )
= $false )
| ~ spl4_4
| ~ spl4_6
| ~ spl4_9 ),
inference(constrained_superposition,[],[f227,f198]) ).
thf(f232,plain,
( ( ( sK1 @ sK0 )
= $false )
| ~ spl4_4
| ~ spl4_6
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f231]) ).
thf(f233,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_9 ),
inference(constrained_superposition,[],[f232,f32]) ).
thf(f237,plain,
( $false
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f233]) ).
thf(f238,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f237]) ).
thf(f240,plain,
( ( $true != $true )
| ( $false
= ( sK2 @ sK0 ) )
| ~ spl4_4
| ~ spl4_11 ),
inference(constrained_superposition,[],[f71,f42]) ).
thf(f241,plain,
( ( $false
= ( sK2 @ sK0 ) )
| ~ spl4_4
| ~ spl4_11 ),
inference(trivial_inequality_removal,[],[f240]) ).
thf(f244,plain,
( ( $true = $false )
| ( ( sK1 @ sK0 )
= $false )
| ~ spl4_4
| ~ spl4_6
| ~ spl4_11 ),
inference(constrained_superposition,[],[f198,f241]) ).
thf(f245,plain,
( ( ( sK1 @ sK0 )
= $false )
| ~ spl4_4
| ~ spl4_6
| ~ spl4_11 ),
inference(trivial_inequality_removal,[],[f244]) ).
thf(f248,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_11 ),
inference(constrained_superposition,[],[f245,f32]) ).
thf(f252,plain,
( $false
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_11 ),
inference(trivial_inequality_removal,[],[f248]) ).
thf(f253,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_11 ),
inference(avatar_contradiction_clause,[],[f252]) ).
thf(f259,plain,
( ( $true
= ( sK1 @ sK0 ) )
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f16,f46]) ).
thf(f265,plain,
( $false
| spl4_2
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f259,f31]) ).
thf(f266,plain,
( spl4_2
| spl4_5 ),
inference(avatar_contradiction_clause,[],[f265]) ).
cnf(s15,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f33]) ).
cnf(s19,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f38]) ).
cnf(s27,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f48]) ).
cnf(s31,plain,
( spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f53]) ).
cnf(s36,plain,
( ~ spl4_3
| spl4_9
| spl4_11 ),
inference(sat_conversion,[],[f72]) ).
cnf(s57,plain,
( ~ spl4_1
| ~ spl4_5
| ~ spl4_9 ),
inference(sat_conversion,[],[f117]) ).
cnf(s81,plain,
( ~ spl4_1
| ~ spl4_5
| ~ spl4_11 ),
inference(sat_conversion,[],[f180]) ).
cnf(s94,plain,
( spl4_1
| spl4_4 ),
inference(sat_conversion,[],[f190]) ).
cnf(s103,plain,
( spl4_1
| spl4_6 ),
inference(sat_conversion,[],[f191]) ).
cnf(s108,plain,
( spl4_3
| spl4_6 ),
inference(sat_conversion,[],[f193]) ).
cnf(s123,plain,
( ~ spl4_2
| spl4_3
| ~ spl4_6 ),
inference(sat_conversion,[],[f224]) ).
cnf(s140,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_9 ),
inference(sat_conversion,[],[f238]) ).
cnf(s151,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_6
| ~ spl4_11 ),
inference(sat_conversion,[],[f253]) ).
cnf(s166,plain,
( spl4_2
| spl4_5 ),
inference(sat_conversion,[],[f266]) ).
cnf(s167,plain,
( ~ spl4_6
| ~ spl4_4
| ~ spl4_2 ),
inference(rat,[],[s36,s123,s140,s151]) ).
cnf(s168,plain,
spl4_1,
inference(rat,[],[s167,s15,s94,s103]) ).
cnf(s169,plain,
spl4_2,
inference(rat,[],[s36,s57,s81,s19,s166,s168]) ).
cnf(s171,plain,
( ~ spl4_5
| ~ spl4_3 ),
inference(rat,[],[s36,s57,s81,s168]) ).
cnf(s172,plain,
spl4_5,
inference(rat,[],[s167,s27,s31,s169]) ).
cnf(s176,plain,
~ spl4_3,
inference(rat,[],[s171,s172]) ).
cnf(s177,plain,
spl4_6,
inference(rat,[],[s108,s176]) ).
cnf(s179,plain,
$false,
inference(rat,[],[s123,s169,s176,s177]) ).
thf(f267,plain,
$false,
inference(avatar_sat_refutation,[],[s179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV221^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 % Computer : n005.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 15:22:31 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.25 Running first-order model finding
% 0.10/0.25 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
% 0.24/0.31 % (1799426)Will run a generic schedule for satisfiability detection.
% 0.24/0.31 % (1799431)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3930239374_2999 on theBenchmark for (2999ds/0Mi)
% 0.24/0.31 % (1799433)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2920897170:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.24/0.31 % Exception at run slice level
% 0.24/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.24/0.31 % (1799432)% WARNING: option uhcvi not known.
% 0.24/0.31 % (1799433) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1799426-1799433"...
% 0.24/0.31 % (1799433)...printing done.
% 0.24/0.31 % (1799434)dis+10_1_sil=32000:sp=arity:random_seed=917786249:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.24/0.31 % (1799432)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3319309759:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.24/0.31 % (1799433)Refutation found. Thanks to Tanya!
% 0.24/0.31 % SZS status Theorem for theBenchmark
% 0.24/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.31 % (1799433)------------------------------
% 0.24/0.31 % (1799433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.31 % (1799433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.31 % (1799433)CaDiCaL version: 2.1.3
% 0.24/0.31 % (1799433)Termination reason: Refutation
% 0.24/0.31 % (1799433)Time elapsed: 0.011 s
% 0.24/0.31 % (1799433)Peak memory usage: 13 MB
% 0.24/0.31 % (1799433)Instructions burned: 15 (million)
% 0.24/0.31 % (1799426)Success in time 0.047 s
% 0.24/0.31 % Vampire exiting
%------------------------------------------------------------------------------