%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU459^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 08:32:08 AM UTC 2026
% Result : Theorem 0.25s 0.32s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 137 ( 28 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 218 ( 7 ~; 13 |; 0 &; 164 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 90 ( 90 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 46 usr; 5 con; 0-4 aty)
% ( 21 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 63 ( 57 ^; 6 !; 0 ?; 63 :)
% 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,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
sK0: $i > $i > $o ).
thf(f1,axiom,
( subrel
= ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',subrel) ).
thf(f4,axiom,
( infl
= ( ^ [X0: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o] : ( subrel @ X1 @ ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',inflationary) ).
thf(f12,axiom,
( sc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
| ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',symmetric_closure) ).
thf(f30,conjecture,
infl @ sc,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_closure_op_is_inflationary) ).
thf(f31,negated_conjecture,
~ ( infl @ sc ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f32,plain,
( subrel
= ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f33,plain,
( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f36,plain,
( infl
= ( ^ [X0: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o] : ( subrel @ X1 @ ( X0 @ X1 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f37,plain,
( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] : ( subrel @ Y1 @ ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f52,plain,
( sc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
| ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f53,plain,
( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f86,plain,
~ ( infl @ sc ),
inference(rectify,[],[f31]) ).
thf(f87,plain,
( ( infl @ sc )
!= $true ),
inference(fool_elimination,[],[f86]) ).
thf(f88,plain,
( ( infl @ sc )
!= $true ),
inference(flattening,[],[f87]) ).
thf(f89,plain,
( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f92,plain,
( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] : ( subrel @ Y1 @ ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f100,plain,
( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f118,plain,
( ( infl @ sc )
!= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f121,plain,
( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
@ Y1
@ ( Y0 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f92,f89]) ).
thf(f136,plain,
( $true
!= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
@ Y1
@ ( Y0 @ Y1 ) ) )
@ ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(definition_unfolding,[],[f118,f121,f100]) ).
thf(f137,plain,
( $true
!= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f139,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( ( sK0 @ Y0 @ Y1 )
| ( sK0 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( ( sK0 @ Y0 @ Y1 )
| ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( ( sK0 @ sK1 @ Y0 )
| ( sK0 @ Y0 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( ( sK0 @ sK1 @ Y0 )
| ( sK0 @ Y0 @ sK1 ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( $false
= ( ( sK0 @ sK2 @ sK1 )
=> ( ( sK0 @ sK1 @ sK2 )
| ( sK0 @ sK2 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f144,plain,
( $false
= ( ( sK0 @ sK1 @ sK2 )
| ( sK0 @ sK2 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( $true
= ( sK0 @ sK2 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f143]) ).
thf(f146,plain,
( $false
= ( sK0 @ sK2 @ sK1 ) ),
inference(or_proxy_clausification,[],[f144]) ).
thf(f149,plain,
$true = $false,
inference(constrained_superposition,[],[f145,f146]) ).
thf(f150,plain,
$false,
inference(trivial_inequality_removal,[],[f149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU459^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 % Computer : n017.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 13:37:07 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.28 Running first-order model finding
% 0.10/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.25/0.32 % (349801)Will run a generic schedule for satisfiability detection.
% 0.25/0.32 % (349809)dis+10_1_sil=32000:sp=arity:random_seed=1207111461:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.25/0.32 % (349806)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2555286106_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.32 % (349809) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-349801-349809"...
% 0.25/0.32 % Exception at run slice level
% 0.25/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.25/0.32 % (349809)...printing done.
% 0.25/0.32 % (349809)Refutation found. Thanks to Tanya!
% 0.25/0.32 % SZS status Theorem for theBenchmark
% 0.25/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.32 % (349809)------------------------------
% 0.25/0.32 % (349809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.32 % (349809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.32 % (349809)CaDiCaL version: 2.1.3
% 0.25/0.32 % (349809)Termination reason: Refutation
% 0.25/0.32 % (349809)Time elapsed: 0.006 s
% 0.25/0.32 % (349809)Peak memory usage: 12 MB
% 0.25/0.32 % (349809)Instructions burned: 11 (million)
% 0.25/0.32 % (349801)Success in time 0.03 s
% 0.25/0.32 % Vampire exiting
%------------------------------------------------------------------------------