%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU495^1 : 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 : n016.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 08:29:48 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 224 ( 67 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 229 ( 9 ~; 42 |; 2 &; 156 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 45 usr; 5 con; 0-4 aty)
% ( 16 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 59 ( 38 ^; 20 !; 1 ?; 59 :)
% 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,
vAND: $o > $o > $o ).
thf(func_def_31,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_33,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_34,type,
vIMP: $o > $o > $o ).
thf(func_def_35,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vOR: $o > $o > $o ).
thf(func_def_38,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vNOT: $o > $o ).
thf(func_def_41,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
sK0: $i > $i > $o ).
thf(f2,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] : ( X0 @ X2 @ X1 ) )
= inv ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',inverse) ).
thf(f19,axiom,
( total
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
| ( X1 = X2 )
| ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',total) ).
thf(f30,conjecture,
! [X0: $i > $i > $o] :
( ( total @ X0 )
=> ( total @ ( inv @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_of_total_relation_is_total_relation) ).
thf(f31,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( total @ X0 )
=> ( total @ ( inv @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f36,plain,
( total
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
| ( X1 = X2 )
| ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f37,plain,
( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f62,plain,
~ ! [X0: $i > $i > $o] :
( ( total @ X0 )
=> ( total @ ( inv @ X0 ) ) ),
inference(rectify,[],[f31]) ).
thf(f63,plain,
~ ! [X0: $i > $i > $o] :
( ( ( total @ X0 )
= $true )
=> ( ( total @ ( inv @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f62]) ).
thf(f87,plain,
( inv
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( total @ ( inv @ X0 ) )
!= $true )
& ( ( total @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f63]) ).
thf(f89,plain,
( ( ( total @ ( inv @ sK0 ) )
!= $true )
& ( ( total @ sK0 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f88]) ).
thf(f97,plain,
( ( total @ sK0 )
= $true ),
inference(cnf_transformation,[],[f89]) ).
thf(f98,plain,
( ( total @ ( inv @ sK0 ) )
!= $true ),
inference(cnf_transformation,[],[f89]) ).
thf(f107,plain,
( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f120,plain,
( inv
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f138,plain,
( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f98,f107,f120]) ).
thf(f139,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 )
= $true ),
inference(definition_unfolding,[],[f97,f107]) ).
thf(f140,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
| ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f141,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
| ( Y1 = Y0 )
| ( sK0 @ Y1 @ Y0 ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK1 @ Y0 )
| ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK1 @ Y0 )
| ( Y0 = sK1 )
| ( sK0 @ Y0 @ sK1 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( $false
= ( ( sK0 @ sK1 @ sK2 )
| ( sK2 = sK1 )
| ( sK0 @ sK2 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f145,plain,
( $false
= ( sK0 @ sK2 @ sK1 ) ),
inference(or_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( $false
= ( ( sK0 @ sK1 @ sK2 )
| ( sK2 = sK1 ) ) ),
inference(or_proxy_clausification,[],[f144]) ).
thf(f147,plain,
( $false
= ( sK2 = sK1 ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( $false
= ( sK0 @ sK1 @ sK2 ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f149,plain,
sK2 != sK1,
inference(equality_proxy_clausification,[],[f147]) ).
thf(f150,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
| ( Y1 = Y0 )
| ( sK0 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f151,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
| ( Y1 = Y0 )
| ( sK0 @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
| ( Y0 = X1 )
| ( sK0 @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
| ( Y0 = X1 )
| ( sK0 @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
| ( X2 = X1 )
| ( sK0 @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( sK0 @ X2 @ X1 )
| ( X2 = X1 ) ) )
| ( ( sK0 @ X1 @ X2 )
= $true ) ),
inference(or_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X1: $i] :
( ( ( X2 = X1 )
= $true )
| ( $true
= ( sK0 @ X2 @ X1 ) )
| ( ( sK0 @ X1 @ X2 )
= $true ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0 @ X2 @ X1 ) )
| ( ( sK0 @ X1 @ X2 )
= $true )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f156]) ).
thf(f163,plain,
( ( sK2 = sK1 )
| ( $false = $true )
| ( $true
= ( sK0 @ sK1 @ sK2 ) ) ),
inference(constrained_superposition,[],[f157,f145]) ).
thf(f164,plain,
( ( $true
= ( sK0 @ sK1 @ sK2 ) )
| ( sK2 = sK1 ) ),
inference(trivial_inequality_removal,[],[f163]) ).
thf(f168,plain,
( $true
= ( sK0 @ sK1 @ sK2 ) ),
inference(forward_subsumption_resolution,[],[f164,f149]) ).
thf(f172,plain,
$false = $true,
inference(forward_demodulation,[],[f168,f148]) ).
thf(f173,plain,
$false,
inference(trivial_inequality_removal,[],[f172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU495^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n016.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:51:14 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.22/0.29 % (374839)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (374847)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=315371753: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)
% 0.22/0.29 % (374844)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=940355624:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (374845)lrs+10_16_si=on:nwc=1.5:random_seed=2142270853:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.29 % (374846)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3471274369:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (374848)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3549695369:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (374846)Instruction limit reached!
% 0.22/0.29 % (374846)------------------------------
% 0.22/0.29 % (374846)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (374846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (374846)CaDiCaL version: 2.1.3
% 0.22/0.29 % (374846)Termination reason: Instruction limit
% 0.22/0.29 % (374846)Termination phase: Property scanning
% 0.22/0.29 % (374846)Time elapsed: 0.002 s
% 0.22/0.29 % (374846)Peak memory usage: 10 MB
% 0.22/0.29 % (374846)Instructions burned: 4 (million)
% 0.22/0.29 % (374845) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-374839-374845"...
% 0.22/0.29 % (374844) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-374839-374844"...
% 0.22/0.29 % (374845)...printing done.
% 0.22/0.29 % (374844)...printing done.
% 0.22/0.29 % (374849)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=622868760:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.29 % (374845)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (374845)------------------------------
% 0.22/0.29 % (374845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (374845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (374845)CaDiCaL version: 2.1.3
% 0.22/0.29 % (374845)Termination reason: Refutation
% 0.22/0.29 % (374845)Time elapsed: 0.007 s
% 0.22/0.29 % (374845)Peak memory usage: 12 MB
% 0.22/0.29 % (374845)Instructions burned: 12 (million)
% 0.22/0.29 % (374839)Success in time 0.039 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------