%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU459^1 : TPTP v9.3.1. Released v3.6.0.
% 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 08:29:43 AM UTC 2026
% Result : Theorem 0.25s 0.37s
% Output : Refutation 0.27s
% 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,
vAND: $o > $o > $o ).
thf(func_def_33,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_38,type,
vNOT: $o > $o ).
thf(func_def_39,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $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/sandbox2/benchmark/Axioms/SET009^0.ax',subrel) ).
thf(f4,axiom,
( ( ^ [X0: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o] : ( subrel @ X1 @ ( X0 @ X1 ) ) )
= infl ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',inflationary) ).
thf(f12,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
| ( X0 @ X2 @ X1 ) ) )
= sc ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',symmetric_closure) ).
thf(f30,conjecture,
infl @ sc,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_closure_op_is_inflationary) ).
thf(f31,negated_conjecture,
~ ( infl @ sc ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f40,plain,
~ ( infl @ sc ),
inference(rectify,[],[f31]) ).
thf(f41,plain,
( ( infl @ sc )
!= $true ),
inference(fool_elimination,[],[f40]) ).
thf(f62,plain,
( ( ^ [X0: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o] : ( subrel @ X1 @ ( X0 @ X1 ) ) )
= infl ),
inference(rectify,[],[f4]) ).
thf(f63,plain,
( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] : ( subrel @ Y1 @ ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f64,plain,
( ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
| ( X0 @ X2 @ X1 ) ) )
= sc ),
inference(rectify,[],[f12]) ).
thf(f65,plain,
( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f64]) ).
thf(f68,plain,
( subrel
= ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f69,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,[],[f68]) ).
thf(f88,plain,
( ( infl @ sc )
!= $true ),
inference(flattening,[],[f41]) ).
thf(f89,plain,
( ( infl @ sc )
!= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f96,plain,
( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] : ( subrel @ Y1 @ ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f107,plain,
( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f118,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,[],[f69]) ).
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,[],[f96,f118]) ).
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,[],[f89,f121,f107]) ).
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(f148,plain,
$true = $false,
inference(forward_demodulation,[],[f146,f145]) ).
thf(f149,plain,
$false,
inference(trivial_inequality_removal,[],[f148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU459^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 % Computer : n003.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Tue Sep 29 13:43:29 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.28 Running higher-order theorem proving
% 0.25/0.30 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
% 0.25/0.37 % (2518107)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.37 % (2518116)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=203575070:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.25/0.37 % (2518118)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.37 % (2518118)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.25/0.37 % (2518114)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3714120386:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.25/0.37 % (2518113)lrs+10_16_si=on:nwc=1.5:random_seed=2110484289:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.37 % (2518112)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1095485246:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.25/0.37 % (2518116)Instruction limit reached!
% 0.25/0.37 % (2518116)------------------------------
% 0.25/0.37 % (2518116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.37 % (2518116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.37 % (2518116)CaDiCaL version: 2.1.3
% 0.25/0.37 % (2518116)Termination reason: Instruction limit
% 0.25/0.37 % (2518116)Termination phase: Saturation
% 0.25/0.37 % (2518116)Time elapsed: 0.013 s
% 0.25/0.37 % (2518116)Peak memory usage: 12 MB
% 0.25/0.37 % (2518116)Instructions burned: 26 (million)
% 0.25/0.37 % (2518117)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=667966041:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.25/0.37 % (2518118)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=52016070:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.25/0.37 % (2518115)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2881050448:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.25/0.37 % (2518114)Instruction limit reached!
% 0.25/0.37 % (2518114)------------------------------
% 0.25/0.37 % (2518114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.37 % (2518114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.37 % (2518114)CaDiCaL version: 2.1.3
% 0.25/0.37 % (2518114)Termination reason: Instruction limit
% 0.25/0.37 % (2518114)Termination phase: Property scanning
% 0.25/0.37 % (2518114)Time elapsed: 0.003 s
% 0.25/0.37 % (2518114)Peak memory usage: 10 MB
% 0.25/0.37 % (2518114)Instructions burned: 3 (million)
% 0.25/0.37 % (2518113) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2518107-2518113"...
% 0.25/0.37 % (2518112) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2518107-2518112"...
% 0.25/0.37 % (2518117) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2518107-2518117"...
% 0.25/0.37 % (2518118) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2518107-2518118"...
% 0.25/0.37 % (2518113)...printing done.
% 0.25/0.37 % (2518112)...printing done.
% 0.25/0.37 % (2518112)Refutation found. Thanks to Tanya!
% 0.25/0.37 % SZS status Theorem for theBenchmark
% 0.25/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.27/0.37 % (2518112)------------------------------
% 0.27/0.37 % (2518112)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.37 % (2518112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.37 % (2518112)CaDiCaL version: 2.1.3
% 0.27/0.37 % (2518112)Termination reason: Refutation
% 0.27/0.37 % (2518112)Time elapsed: 0.011 s
% 0.27/0.37 % (2518112)Peak memory usage: 12 MB
% 0.27/0.37 % (2518112)Instructions burned: 12 (million)
% 0.27/0.37 % (2518107)Success in time 0.06 s
% 0.27/0.37 % Vampire exiting
%------------------------------------------------------------------------------