%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU800^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:31:29 AM UTC 2026
% Result : Theorem 0.24s 0.36s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 21 unt; 0 typ; 5 def)
% Number of atoms : 286 ( 72 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 373 ( 55 ~; 46 |; 12 &; 242 @)
% ( 7 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 13 con; 0-4 aty)
% Number of variables : 99 ( 0 sgn 54 !; 12 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
dsetconstrER: $o ).
thf(func_def_4,type,
funcSet: $i > $i > $i ).
thf(func_def_5,type,
injective: $i > $i > $i > $o ).
thf(func_def_6,type,
injFuncSet: $i > $i > $i ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK4: $i > $o ).
thf(func_def_19,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X1: $i > $o,X0: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f2,axiom,
( injFuncSet
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( funcSet @ X0 @ X1 )
@ ^ [X2: $i] : ( injective @ X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injFuncSet) ).
thf(f3,conjecture,
( dsetconstrER
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ ( injFuncSet @ X0 @ X1 ) )
=> ( injective @ X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injFuncSetFuncInj) ).
thf(f4,negated_conjecture,
~ ( dsetconstrER
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ ( injFuncSet @ X0 @ X1 ) )
=> ( injective @ X0 @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( X0 @ X2 ) )
= dsetconstrER ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
=> ( $true
= ( X0 @ X2 ) ) )
<=> ( dsetconstrER = $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( injFuncSet @ X1 @ X2 ) )
=> ( injective @ X1 @ X2 @ X0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ( ( dsetconstrER = $true )
=> ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( injFuncSet @ X1 @ X2 ) ) )
=> ( $true
= ( injective @ X1 @ X2 @ X0 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( injFuncSet
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( funcSet @ X0 @ X1 )
@ ^ [X2: $i] : ( injective @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( injFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( injective @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( dsetconstrER = $true )
& ? [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( injective @ X1 @ X2 @ X0 ) )
& ( $true
= ( in @ X0 @ ( injFuncSet @ X1 @ X2 ) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
( ( dsetconstrER = $true )
<=> ! [X1: $i,X0: $i > $o,X2: $i] :
( ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( $true
= ( X0 @ X2 ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f13,plain,
( ( dsetconstrER = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( injective @ X1 @ X0 @ X2 ) )
& ( ( in @ X2 @ ( injFuncSet @ X1 @ X0 ) )
= $true ) ) ),
inference(rectify,[],[f11]) ).
thf(f14,plain,
( ( dsetconstrER = $true )
& ( $true
!= ( injective @ sK1 @ sK0 @ sK2 ) )
& ( $true
= ( in @ sK2 @ ( injFuncSet @ sK1 @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f13]) ).
thf(f15,plain,
( ( ( dsetconstrER = $true )
| ? [X1: $i,X0: $i > $o,X2: $i] :
( ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( $true
!= ( X0 @ X2 ) ) ) )
& ( ! [X1: $i,X0: $i > $o,X2: $i] :
( ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( $true
= ( X0 @ X2 ) ) )
| ( dsetconstrER != $true ) ) ),
inference(nnf_transformation,[],[f12]) ).
thf(f16,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( $true
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
& ( ( X1 @ X2 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( $true
!= ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) ) )
| ( $true
= ( X4 @ X5 ) ) )
| ( dsetconstrER != $true ) ) ),
inference(rectify,[],[f15]) ).
thf(f17,plain,
( ( ( dsetconstrER = $true )
| ( ( $true
= ( in @ sK5
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( sK4 @ Y0 ) ) ) )
& ( $true
!= ( sK4 @ sK5 ) ) ) )
& ( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( $true
!= ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) ) )
| ( $true
= ( X4 @ X5 ) ) )
| ( dsetconstrER != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f16]) ).
thf(f18,plain,
( injFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( injective @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f19,plain,
( $true
= ( in @ sK2 @ ( injFuncSet @ sK1 @ sK0 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f20,plain,
( $true
!= ( injective @ sK1 @ sK0 @ sK2 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f22,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( $true
!= ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) ) )
| ( dsetconstrER != $true )
| ( $true
= ( X4 @ X5 ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f26,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( $true
= ( X4 @ X5 ) )
| ( $true
!= ( in @ X5 @ ( dsetconstr @ X3 @ X4 ) ) )
| ( dsetconstrER != $true ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f28,plain,
( injFuncSet
= ( ^ [Y0: $i,Y1: $i] : ( dsetconstr @ ( funcSet @ Y0 @ Y1 ) @ ( injective @ Y0 @ Y1 ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f30,definition,
( spl6_1
<=> ( dsetconstrER = $true ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f34,definition,
( spl6_2
<=> ! [X4: $i > $o,X5: $i,X3: $i] :
( ( $true
= ( X4 @ X5 ) )
| ( $true
!= ( in @ X5 @ ( dsetconstr @ X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f35,plain,
( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( $true
!= ( in @ X5 @ ( dsetconstr @ X3 @ X4 ) ) )
| ( $true
= ( X4 @ X5 ) ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f36,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f26,f34,f30]) ).
thf(f37,plain,
spl6_1,
inference(avatar_split_clause,[],[f21,f30]) ).
thf(f39,definition,
( spl6_3
<=> ( $true
= ( injective @ sK1 @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f41,plain,
( ( $true
!= ( injective @ sK1 @ sK0 @ sK2 ) )
| spl6_3 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f42,plain,
~ spl6_3,
inference(avatar_split_clause,[],[f20,f39]) ).
thf(f49,definition,
( spl6_5
<=> ( $true
= ( in @ sK2 @ ( injFuncSet @ sK1 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f51,plain,
( ( $true
= ( in @ sK2 @ ( injFuncSet @ sK1 @ sK0 ) ) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f52,plain,
spl6_5,
inference(avatar_split_clause,[],[f19,f49]) ).
thf(f59,definition,
( spl6_7
<=> ( injFuncSet
= ( ^ [Y0: $i,Y1: $i] : ( dsetconstr @ ( funcSet @ Y0 @ Y1 ) @ ( injective @ Y0 @ Y1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
thf(f61,plain,
( ( injFuncSet
= ( ^ [Y0: $i,Y1: $i] : ( dsetconstr @ ( funcSet @ Y0 @ Y1 ) @ ( injective @ Y0 @ Y1 ) ) ) )
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f62,plain,
spl6_7,
inference(avatar_split_clause,[],[f28,f59]) ).
thf(f64,plain,
( ! [X1: $i] :
( ( injFuncSet @ X1 )
= ( ^ [Y0: $i,Y1: $i] : ( dsetconstr @ ( funcSet @ Y0 @ Y1 ) @ ( injective @ Y0 @ Y1 ) )
@ X1 ) )
| ~ spl6_7 ),
inference(argument_congruence,[],[f61]) ).
thf(f65,plain,
( ! [X1: $i] :
( ( injFuncSet @ X1 )
= ( ^ [Y0: $i] : ( dsetconstr @ ( funcSet @ X1 @ Y0 ) @ ( injective @ X1 @ Y0 ) ) ) )
| ~ spl6_7 ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
( ! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] : ( dsetconstr @ ( funcSet @ X1 @ Y0 ) @ ( injective @ X1 @ Y0 ) )
@ X2 )
= ( injFuncSet @ X1 @ X2 ) )
| ~ spl6_7 ),
inference(argument_congruence,[],[f65]) ).
thf(f67,plain,
( ! [X2: $i,X1: $i] :
( ( dsetconstr @ ( funcSet @ X1 @ X2 ) @ ( injective @ X1 @ X2 ) )
= ( injFuncSet @ X1 @ X2 ) )
| ~ spl6_7 ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f68,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( injFuncSet @ X0 @ X1 ) )
!= $true )
| ( ( injective @ X0 @ X1 @ X2 )
= $true ) )
| ~ spl6_2
| ~ spl6_7 ),
inference(superposition,[],[f35,f67]) ).
thf(f69,plain,
( ( $true
= ( injective @ sK1 @ sK0 @ sK2 ) )
| ( $true != $true )
| ~ spl6_2
| ~ spl6_5
| ~ spl6_7 ),
inference(superposition,[],[f68,f51]) ).
thf(f70,plain,
( ( $true
= ( injective @ sK1 @ sK0 @ sK2 ) )
| ~ spl6_2
| ~ spl6_5
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f71,plain,
( $false
| ~ spl6_2
| spl6_3
| ~ spl6_5
| ~ spl6_7 ),
inference(forward_subsumption_resolution,[],[f70,f41]) ).
thf(f72,plain,
( ~ spl6_2
| spl6_3
| ~ spl6_5
| ~ spl6_7 ),
inference(avatar_contradiction_clause,[],[f71]) ).
cnf(s1,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f36]) ).
cnf(s2,plain,
spl6_1,
inference(sat_conversion,[],[f37]) ).
cnf(s3,plain,
~ spl6_3,
inference(sat_conversion,[],[f42]) ).
cnf(s5,plain,
spl6_5,
inference(sat_conversion,[],[f52]) ).
cnf(s7,plain,
spl6_7,
inference(sat_conversion,[],[f62]) ).
cnf(s8,plain,
( ~ spl6_2
| spl6_3
| ~ spl6_5
| ~ spl6_7 ),
inference(sat_conversion,[],[f72]) ).
cnf(s9,plain,
~ spl6_2,
inference(rat,[],[s8,s7,s5,s3]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s9,s2]) ).
thf(f73,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU800^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.27 % Computer : n018.cluster.edu
% 0.24/0.27 % Model : x86_64 x86_64
% 0.24/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.27 % Memory : 8046.5625MB
% 0.24/0.27 % OS : Linux 6.8.0-71-generic
% 0.24/0.27 % CPULimit : 300
% 0.24/0.27 % WCLimit : 300
% 0.24/0.27 % DateTime : Tue Sep 29 14:34:12 UTC 2026
% 0.24/0.27 % CPUTime :
% 0.24/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.32 Running higher-order theorem proving
% 0.24/0.33 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
% 0.24/0.36 % (163117)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.36 % (163125)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=1884725699: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)
% 0.24/0.36 % (163125) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-163117-163125"...
% 0.24/0.36 % (163125)...printing done.
% 0.24/0.36 % (163125)Refutation found. Thanks to Tanya!
% 0.24/0.36 % SZS status Theorem for theBenchmark
% 0.24/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.36 % (163125)------------------------------
% 0.24/0.36 % (163125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.36 % (163125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.36 % (163125)CaDiCaL version: 2.1.3
% 0.24/0.36 % (163125)Termination reason: Refutation
% 0.24/0.36 % (163125)Time elapsed: 0.002 s
% 0.24/0.36 % (163125)Peak memory usage: 13 MB
% 0.24/0.36 % (163125)Instructions burned: 5 (million)
% 0.24/0.36 % (163117)Success in time 0.017 s
% 0.24/0.36 % Vampire exiting
%------------------------------------------------------------------------------