%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU675^2 : 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 : 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 08:30:41 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 22 unt; 0 typ; 5 def)
% Number of atoms : 287 ( 72 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 384 ( 55 ~; 46 |; 12 &; 253 @)
% ( 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 : 41 ( 38 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_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
powerset: $i > $i ).
thf(func_def_4,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_5,type,
dsetconstrER: $o ).
thf(func_def_7,type,
subset: $i > $i > $o ).
thf(func_def_8,type,
kpair: $i > $i > $i ).
thf(func_def_9,type,
cartprod: $i > $i > $i ).
thf(func_def_10,type,
singleton: $i > $o ).
thf(func_def_11,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_12,type,
breln: $i > $i > $i > $o ).
thf(func_def_13,type,
func: $i > $i > $i > $o ).
thf(func_def_14,type,
funcSet: $i > $i > $i ).
thf(func_def_17,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
vAND: $o > $o > $o ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_23,type,
vIMP: $o > $o > $o ).
thf(func_def_24,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_32,type,
sK5: $i > $o ).
thf(func_def_33,type,
vNOT: $o > $o ).
thf(func_def_35,type,
sK7: $i > $i ).
thf(func_def_36,type,
sK8: $i > $i > $i > $i ).
thf(f1,axiom,
( dsetconstrER
= ( ! [X2: $i,X0: $i,X1: $i > $o] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f6,axiom,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X0 @ X1 ) )
@ ^ [X2: $i] : ( func @ X0 @ X1 @ X2 ) ) )
= funcSet ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcSet) ).
thf(f7,conjecture,
( dsetconstrER
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(f8,negated_conjecture,
~ ( dsetconstrER
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( funcSet @ X0 @ X2 ) )
=> ( func @ X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f8]) ).
thf(f10,plain,
~ ( ( dsetconstrER = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) )
=> ( $true
= ( func @ X0 @ X2 @ X1 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f15,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( X2 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f16,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
=> ( $true
= ( X2 @ X0 ) ) )
<=> ( dsetconstrER = $true ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X0 @ X1 ) )
@ ^ [X2: $i] : ( func @ X0 @ X1 @ X2 ) ) )
= funcSet ),
inference(rectify,[],[f6]) ).
thf(f18,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] : ( func @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f22,plain,
( ( dsetconstrER = $true )
<=> ! [X1: $i,X0: $i,X2: $i > $o] :
( ( $true
= ( X2 @ X0 ) )
| ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f23,plain,
( ( dsetconstrER = $true )
& ? [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) )
& ( $true
!= ( func @ X0 @ X2 @ X1 ) ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f24,plain,
( ( dsetconstrER = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( funcSet @ X1 @ X2 ) ) )
& ( $true
!= ( func @ X1 @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f25,plain,
( ( dsetconstrER = $true )
& ( $true
= ( in @ sK0 @ ( funcSet @ sK1 @ sK2 ) ) )
& ( ( func @ sK1 @ sK2 @ sK0 )
!= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f24]) ).
thf(f26,plain,
( ( ( dsetconstrER = $true )
| ? [X1: $i,X0: $i,X2: $i > $o] :
( ( $true
!= ( X2 @ X0 ) )
& ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true ) ) )
& ( ! [X1: $i,X0: $i,X2: $i > $o] :
( ( $true
= ( X2 @ X0 ) )
| ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(nnf_transformation,[],[f22]) ).
thf(f27,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( X2 @ X1 ) )
& ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( X5 @ X4 )
= $true )
| ( $true
!= ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) ) ),
inference(rectify,[],[f26]) ).
thf(f28,plain,
( ( ( dsetconstrER = $true )
| ( ( ( sK5 @ sK4 )
!= $true )
& ( $true
= ( in @ sK4
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( sK5 @ Y0 ) ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( X5 @ X4 )
= $true )
| ( $true
!= ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f27]) ).
thf(f29,plain,
( ( func @ sK1 @ sK2 @ sK0 )
!= $true ),
inference(cnf_transformation,[],[f25]) ).
thf(f30,plain,
( $true
= ( in @ sK0 @ ( funcSet @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f31,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f35,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( X5 @ X4 )
= $true )
| ( $true
!= ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f39,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] : ( func @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f41,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] : ( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) ) @ ( func @ Y0 @ Y1 ) ) ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f44,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( X5 @ X4 )
= $true )
| ( ( in @ X4 @ ( dsetconstr @ X3 @ X5 ) )
!= $true )
| ( dsetconstrER != $true ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f46,definition,
( spl6_1
<=> ( dsetconstrER = $true ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f55,definition,
( spl6_3
<=> ( funcSet
= ( ^ [Y0: $i,Y1: $i] : ( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) ) @ ( func @ Y0 @ Y1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f57,plain,
( ( funcSet
= ( ^ [Y0: $i,Y1: $i] : ( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) ) @ ( func @ Y0 @ Y1 ) ) ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f58,plain,
spl6_3,
inference(avatar_split_clause,[],[f41,f55]) ).
thf(f60,definition,
( spl6_4
<=> ( ( func @ sK1 @ sK2 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f62,plain,
( ( ( func @ sK1 @ sK2 @ sK0 )
!= $true )
| spl6_4 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f63,plain,
~ spl6_4,
inference(avatar_split_clause,[],[f29,f60]) ).
thf(f79,plain,
spl6_1,
inference(avatar_split_clause,[],[f31,f46]) ).
thf(f86,definition,
( spl6_9
<=> ! [X4: $i,X5: $i > $o,X3: $i] :
( ( ( X5 @ X4 )
= $true )
| ( ( in @ X4 @ ( dsetconstr @ X3 @ X5 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
thf(f87,plain,
( ! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X4 @ ( dsetconstr @ X3 @ X5 ) )
!= $true )
| ( ( X5 @ X4 )
= $true ) )
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f86]) ).
thf(f88,plain,
( ~ spl6_1
| spl6_9 ),
inference(avatar_split_clause,[],[f44,f86,f46]) ).
thf(f95,definition,
( spl6_11
<=> ( $true
= ( in @ sK0 @ ( funcSet @ sK1 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition]) ).
thf(f97,plain,
( ( $true
= ( in @ sK0 @ ( funcSet @ sK1 @ sK2 ) ) )
| ~ spl6_11 ),
inference(avatar_component_clause,[],[f95]) ).
thf(f98,plain,
spl6_11,
inference(avatar_split_clause,[],[f30,f95]) ).
thf(f104,plain,
( ! [X1: $i] :
( ( funcSet @ X1 )
= ( ^ [Y0: $i,Y1: $i] : ( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) ) @ ( func @ Y0 @ Y1 ) )
@ X1 ) )
| ~ spl6_3 ),
inference(argument_congruence,[],[f57]) ).
thf(f105,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : ( dsetconstr @ ( powerset @ ( cartprod @ X1 @ Y0 ) ) @ ( func @ X1 @ Y0 ) ) )
= ( funcSet @ X1 ) )
| ~ spl6_3 ),
inference(beta-eta_normalization,[],[f104]) ).
thf(f157,plain,
( ! [X2: $i,X1: $i] :
( ( funcSet @ X1 @ X2 )
= ( ^ [Y0: $i] : ( dsetconstr @ ( powerset @ ( cartprod @ X1 @ Y0 ) ) @ ( func @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl6_3 ),
inference(argument_congruence,[],[f105]) ).
thf(f158,plain,
( ! [X2: $i,X1: $i] :
( ( dsetconstr @ ( powerset @ ( cartprod @ X1 @ X2 ) ) @ ( func @ X1 @ X2 ) )
= ( funcSet @ X1 @ X2 ) )
| ~ spl6_3 ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f161,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
!= $true )
| ( ( func @ X0 @ X1 @ X2 )
= $true ) )
| ~ spl6_3
| ~ spl6_9 ),
inference(superposition,[],[f87,f158]) ).
thf(f179,plain,
( ( $true != $true )
| ( ( func @ sK1 @ sK2 @ sK0 )
= $true )
| ~ spl6_3
| ~ spl6_9
| ~ spl6_11 ),
inference(superposition,[],[f161,f97]) ).
thf(f183,plain,
( ( ( func @ sK1 @ sK2 @ sK0 )
= $true )
| ~ spl6_3
| ~ spl6_9
| ~ spl6_11 ),
inference(trivial_inequality_removal,[],[f179]) ).
thf(f184,plain,
( $false
| ~ spl6_3
| spl6_4
| ~ spl6_9
| ~ spl6_11 ),
inference(forward_subsumption_resolution,[],[f183,f62]) ).
thf(f185,plain,
( ~ spl6_3
| spl6_4
| ~ spl6_9
| ~ spl6_11 ),
inference(avatar_contradiction_clause,[],[f184]) ).
cnf(s2,plain,
spl6_3,
inference(sat_conversion,[],[f58]) ).
cnf(s3,plain,
~ spl6_4,
inference(sat_conversion,[],[f63]) ).
cnf(s7,plain,
spl6_1,
inference(sat_conversion,[],[f79]) ).
cnf(s9,plain,
( ~ spl6_1
| spl6_9 ),
inference(sat_conversion,[],[f88]) ).
cnf(s11,plain,
spl6_11,
inference(sat_conversion,[],[f98]) ).
cnf(s14,plain,
( ~ spl6_3
| spl6_4
| ~ spl6_9
| ~ spl6_11 ),
inference(sat_conversion,[],[f185]) ).
cnf(s15,plain,
spl6_9,
inference(rat,[],[s9,s7]) ).
cnf(s16,plain,
~ spl6_3,
inference(rat,[],[s14,s11,s15,s3]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s2,s16]) ).
thf(f186,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU675^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n013.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 14:06:51 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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
% 0.19/0.26 % (2171721)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.26 % (2171729)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=848042959: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)
% 0.19/0.26 % (2171729) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2171721-2171729"...
% 0.19/0.26 % (2171729)...printing done.
% 0.19/0.26 % (2171729)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (2171729)------------------------------
% 0.19/0.27 % (2171729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (2171729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (2171729)CaDiCaL version: 2.1.3
% 0.19/0.27 % (2171729)Termination reason: Refutation
% 0.19/0.27 % (2171729)Time elapsed: 0.006 s
% 0.19/0.27 % (2171729)Peak memory usage: 13 MB
% 0.19/0.27 % (2171729)Instructions burned: 13 (million)
% 0.19/0.27 % (2171721)Success in time 0.032 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------