%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU484^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 08:32:10 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 3
% Syntax : Number of formulae : 42 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 197 ( 66 equ; 1 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 328 ( 31 ~; 20 |; 14 &; 201 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 44 usr; 5 con; 0-4 aty)
% ( 19 !!; 15 ??; 0 @@+; 0 @@-)
% Number of variables : 101 ( 44 ^; 52 !; 5 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_2,type,
inv: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_3,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_4,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_5,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_6,type,
refl: ( $i > $i > $o ) > $o ).
thf(func_def_7,type,
irrefl: ( $i > $i > $o ) > $o ).
thf(func_def_8,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_9,type,
symm: ( $i > $i > $o ) > $o ).
thf(func_def_10,type,
antisymm: ( $i > $i > $o ) > $o ).
thf(func_def_11,type,
asymm: ( $i > $i > $o ) > $o ).
thf(func_def_12,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_13,type,
trans: ( $i > $i > $o ) > $o ).
thf(func_def_14,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_15,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_16,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_17,type,
po: ( $i > $i > $o ) > $o ).
thf(func_def_18,type,
so: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
total: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
term: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
ind: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
innf: ( $i > $i > $o ) > $i > $o ).
thf(func_def_23,type,
nfof: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_24,type,
norm: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
join: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_26,type,
lconfl: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
sconfl: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
confl: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
cr: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vIMP: $o > $o > $o ).
thf(func_def_32,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_37,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_38,type,
vNOT: $o > $o ).
thf(func_def_39,type,
vOR: $o > $o > $o ).
thf(func_def_40,type,
vAND: $o > $o > $o ).
thf(func_def_41,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
sK0: $i > $i > $o ).
thf(func_def_45,type,
sK1: ( $i > $o ) > $i ).
thf(f6,axiom,
( refl
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',reflexive) ).
thf(f20,axiom,
( term
= ( ^ [X0: $i > $i > $o] :
! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ( X0 @ X2 @ X3 ) )
& ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',terminating) ).
thf(f30,conjecture,
! [X0: $i > $i > $o] :
( ( refl @ X0 )
=> ~ ( term @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexive_implies_non_terminating) ).
thf(f31,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( refl @ X0 )
=> ~ ( term @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f40,plain,
( refl
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f6]) ).
thf(f41,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f66,plain,
( term
= ( ^ [X0: $i > $i > $o] :
! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ? [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X4 )
=> ~ ( X0 @ X3 @ X4 ) )
& ( X1 @ X3 ) ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f67,plain,
( term
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f86,plain,
~ ! [X0: $i > $i > $o] :
( ( refl @ X0 )
=> ~ ( term @ X0 ) ),
inference(rectify,[],[f31]) ).
thf(f87,plain,
~ ! [X0: $i > $i > $o] :
( ( ( refl @ X0 )
= $true )
=> ( ( term @ X0 )
!= $true ) ),
inference(fool_elimination,[],[f86]) ).
thf(f88,plain,
~ ! [X0: $i > $i > $o] :
( ( ( refl @ X0 )
= $true )
=> ( ( term @ X0 )
!= $true ) ),
inference(flattening,[],[f87]) ).
thf(f89,plain,
? [X0: $i > $i > $o] :
( ( ( term @ X0 )
= $true )
& ( ( refl @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f88]) ).
thf(f90,plain,
( ( $true
= ( term @ sK0 ) )
& ( $true
= ( refl @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f89]) ).
thf(f96,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f110,plain,
( term
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f120,plain,
( $true
= ( refl @ sK0 ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f121,plain,
( $true
= ( term @ sK0 ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f139,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f121,f110]) ).
thf(f140,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f120,f96]) ).
thf(f141,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X1: $i] :
( $true
= ( sK0 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f144,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ~ ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f145,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ~ ( sK0 @ Y1 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X1: $i > $o] :
( $true
= ( ( ?? @ $i @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
! [X1: $i > $o] :
( ( $false
= ( ?? @ $i @ X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $false )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( X1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) )
@ ( sK1 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $false )
| ( $true
= ( ( X1 @ ( sK1 @ X1 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ~ ( sK0 @ ( sK1 @ X1 ) @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ~ ( sK0 @ ( sK1 @ X1 ) @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $false )
| ( $true
= ( X1 @ ( sK1 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f150]) ).
thf(f153,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ~ ( sK0 @ ( sK1 @ X1 ) @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f151]) ).
thf(f154,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $false )
| ( $true
= ( ( X1 @ X3 )
=> ~ ( sK0 @ ( sK1 @ X1 ) @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $false )
| ( ( X1 @ X3 )
= $false )
| ( $true
= ( ~ ( sK0 @ ( sK1 @ X1 ) @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( sK0 @ ( sK1 @ X1 ) @ X3 ) )
| ( ( X1 @ X2 )
= $false )
| ( ( X1 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f155]) ).
thf(f164,plain,
! [X0: $i] :
( ( sK1 @ ( (=) @ X0 ) )
= X0 ),
inference(leibniz_equality_elimination,[],[f152]) ).
thf(f317,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $false
= ( X0 = X2 ) )
| ( $false
= ( X0 = X1 ) ) ),
inference(constrained_superposition,[],[f156,f164]) ).
thf(f321,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X1 ) )
| ( X0 != X2 )
| ( $false
= ( X0 = X1 ) ) ),
inference(equality_proxy_clausification,[],[f317]) ).
thf(f322,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X1 ) )
| ( X0 != X2 )
| ( X0 != X1 ) ),
inference(equality_proxy_clausification,[],[f321]) ).
thf(f365,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( X0 != X1 )
| ( X0 != X0 ) ),
inference(constrained_superposition,[],[f143,f322]) ).
thf(f372,plain,
! [X0: $i,X1: $i] : ( X0 != X1 ),
inference(trivial_inequality_removal,[],[f365]) ).
thf(f373,plain,
$false,
inference(flex-flex_simplification,[],[f372]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU484^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n013.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:42:51 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.20/0.28 % (2131517)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (2131523)% WARNING: option uhcvi not known.
% 0.20/0.28 % (2131523)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=985992240:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (2131523)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (2131523)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.28 % (2131522)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2155932071_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (2131526)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1125117861:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (2131526)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (2131523) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2131517-2131523"...
% 0.20/0.28 % (2131524)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2471548052:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (2131523)...printing done.
% 0.20/0.28 % (2131523)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (2131523)------------------------------
% 0.20/0.28 % (2131523)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (2131523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (2131523)CaDiCaL version: 2.1.3
% 0.20/0.28 % (2131523)Termination reason: Refutation
% 0.20/0.28 % (2131523)Time elapsed: 0.013 s
% 0.20/0.28 % (2131523)Peak memory usage: 12 MB
% 0.20/0.28 % (2131523)Instructions burned: 23 (million)
% 0.20/0.28 % (2131517)Success in time 0.046 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------