%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU777^2 : 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 : 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 08:31:18 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 251 ( 54 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 515 ( 7 ~; 2 |; 15 &; 421 @)
% ( 0 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 23 usr; 8 con; 0-4 aty)
% ( 35 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 147 ( 78 ^; 61 !; 8 ?; 147 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
kpair: $i > $i > $i ).
thf(func_def_3,type,
cartprod: $i > $i > $i ).
thf(func_def_4,type,
breln: $i > $i > $i > $o ).
thf(func_def_6,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_7,type,
dpsetconstrER: $o ).
thf(func_def_8,type,
breln1: $i > $i > $o ).
thf(func_def_9,type,
breln1invset: $i > $i > $i ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_14,type,
vIMP: $o > $o > $o ).
thf(func_def_15,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(f2,axiom,
( dpsetconstrER
= ( ! [X0: $i,X2: $i > $i > $o,X3: $i,X1: $i,X4: $i] :
( ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [X5: $i,X6: $i] : ( X2 @ X5 @ X6 ) ) )
=> ( X2 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(f4,axiom,
( breln1invset
= ( ^ [X0: $i,X1: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X2: $i,X3: $i] : ( in @ ( kpair @ X3 @ X2 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1invset) ).
thf(f5,conjecture,
( dpsetconstrER
=> ! [X1: $i,X0: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) )
=> ( in @ ( kpair @ X2 @ X3 ) @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1invE) ).
thf(f6,negated_conjecture,
~ ( dpsetconstrER
=> ! [X1: $i,X0: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) )
=> ( in @ ( kpair @ X2 @ X3 ) @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f8,plain,
( dpsetconstrER
= ( ! [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i,X4: $i] :
( ( in @ ( kpair @ X2 @ X4 )
@ ( dpsetconstr @ X0 @ X3
@ ^ [X5: $i,X6: $i] : ( X1 @ X5 @ X6 ) ) )
=> ( X1 @ X2 @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( dpsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( in @ ( kpair @ Y2 @ Y0 )
@ ( dpsetconstr @ Y4 @ Y1
@ ^ [Y5: $i,Y6: $i] : ( Y3 @ Y5 @ Y6 ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f11,plain,
( breln1invset
= ( ^ [X0: $i,X1: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X2: $i,X3: $i] : ( in @ ( kpair @ X3 @ X2 ) @ X1 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f12,plain,
( breln1invset
= ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
~ ( dpsetconstrER
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X1 @ X0 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X1 @ X0 ) )
=> ( in @ ( kpair @ X2 @ X3 ) @ X0 ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f14,plain,
~ ( ( dpsetconstrER = $true )
=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X1 @ X0 ) )
= $true )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X0 )
= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ ( kpair @ X2 @ X3 ) @ X0 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X1 @ X0 ) )
= $true )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( ( breln1 @ X1 @ X0 )
= $true ) )
& ( dpsetconstrER = $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X1 @ X0 ) )
= $true )
& ( ( in @ ( kpair @ X2 @ X3 ) @ X0 )
!= $true ) ) ) )
& ( dpsetconstrER = $true ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
( ( ( breln1 @ sK1 @ sK0 )
= $true )
& ( ( in @ sK2 @ sK1 )
= $true )
& ( ( in @ sK3 @ sK1 )
= $true )
& ( ( in @ ( kpair @ sK3 @ sK2 ) @ ( breln1invset @ sK1 @ sK0 ) )
= $true )
& ( ( in @ ( kpair @ sK2 @ sK3 ) @ sK0 )
!= $true )
& ( dpsetconstrER = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f16]) ).
thf(f18,plain,
( dpsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( in @ ( kpair @ Y2 @ Y0 )
@ ( dpsetconstr @ Y4 @ Y1
@ ^ [Y5: $i,Y6: $i] : ( Y3 @ Y5 @ Y6 ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f21,plain,
( breln1invset
= ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f22,plain,
dpsetconstrER = $true,
inference(cnf_transformation,[],[f17]) ).
thf(f23,plain,
( ( in @ ( kpair @ sK2 @ sK3 ) @ sK0 )
!= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f24,plain,
( ( in @ ( kpair @ sK3 @ sK2 ) @ ( breln1invset @ sK1 @ sK0 ) )
= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f31,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( in @ ( kpair @ Y2 @ Y0 )
@ ( dpsetconstr @ Y4 @ Y1
@ ^ [Y5: $i,Y6: $i] : ( Y3 @ Y5 @ Y6 ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f18,f22]) ).
thf(f33,plain,
( ( in @ ( kpair @ sK3 @ sK2 )
@ ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) )
@ sK1
@ sK0 ) )
= $true ),
inference(definition_unfolding,[],[f24,f21]) ).
thf(f34,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( in @ ( kpair @ Y2 @ Y0 )
@ ( dpsetconstr @ Y4 @ Y1
@ ^ [Y5: $i,Y6: $i] : ( Y3 @ Y5 @ Y6 ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f35,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ ( kpair @ Y1 @ X1 ) @ ( dpsetconstr @ Y3 @ Y0 @ Y2 ) )
=> ( Y2 @ Y1 @ X1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ ( kpair @ Y1 @ X1 ) @ ( dpsetconstr @ Y3 @ Y0 @ Y2 ) )
=> ( Y2 @ Y1 @ X1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( kpair @ Y0 @ X1 ) @ ( dpsetconstr @ Y2 @ X2 @ Y1 ) )
=> ( Y1 @ Y0 @ X1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ ( kpair @ Y0 @ X1 ) @ ( dpsetconstr @ Y2 @ X2 @ Y1 ) )
=> ( Y1 @ Y0 @ X1 ) ) ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ ( kpair @ X3 @ X1 ) @ ( dpsetconstr @ Y1 @ X2 @ Y0 ) )
=> ( Y0 @ X3 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ ( kpair @ X3 @ X1 ) @ ( dpsetconstr @ Y1 @ X2 @ Y0 ) )
=> ( Y0 @ X3 @ X1 ) ) )
@ X4 )
= $true ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ ( kpair @ X3 @ X1 ) @ ( dpsetconstr @ Y0 @ X2 @ X4 ) )
=> ( X4 @ X3 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $i > $o,X5: $i] :
( ( ^ [Y0: $i] :
( ( in @ ( kpair @ X3 @ X1 ) @ ( dpsetconstr @ Y0 @ X2 @ X4 ) )
=> ( X4 @ X3 @ X1 ) )
@ X5 )
= $true ),
inference(pi_proxy_clausification,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $i > $o,X5: $i] :
( ( ( in @ ( kpair @ X3 @ X1 ) @ ( dpsetconstr @ X5 @ X2 @ X4 ) )
=> ( X4 @ X3 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i > $i > $o,X5: $i] :
( ( $false
= ( in @ ( kpair @ X3 @ X1 ) @ ( dpsetconstr @ X5 @ X2 @ X4 ) ) )
| ( ( X4 @ X3 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f43]) ).
thf(f46,plain,
( ( in @ ( kpair @ sK3 @ sK2 )
@ ( dpsetconstr @ sK1 @ sK1
@ ^ [Y0: $i,Y1: $i] : ( in @ ( kpair @ Y1 @ Y0 ) @ sK0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f51,plain,
( ( $false = $true )
| ( ( ^ [Y0: $i,Y1: $i] : ( in @ ( kpair @ Y1 @ Y0 ) @ sK0 )
@ sK3
@ sK2 )
= $true ) ),
inference(constrained_superposition,[],[f46,f44]) ).
thf(f53,plain,
( ( ^ [Y0: $i,Y1: $i] : ( in @ ( kpair @ Y1 @ Y0 ) @ sK0 )
@ sK3
@ sK2 )
= $true ),
inference(trivial_inequality_removal,[],[f51]) ).
thf(f54,plain,
( ( in @ ( kpair @ sK2 @ sK3 ) @ sK0 )
= $true ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f57,plain,
$false,
inference(forward_subsumption_resolution,[],[f54,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU777^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:29:44 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.09/0.26 % (2584690)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.26 % (2584700)lrs+10_16_si=on:nwc=1.5:random_seed=231088151:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.09/0.26 % (2584700) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2584690-2584700"...
% 0.09/0.26 % (2584700)...printing done.
% 0.09/0.26 % (2584700)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.26 % (2584700)------------------------------
% 0.20/0.26 % (2584700)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (2584700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (2584700)CaDiCaL version: 2.1.3
% 0.20/0.26 % (2584700)Termination reason: Refutation
% 0.20/0.26 % (2584700)Time elapsed: 0.002 s
% 0.20/0.26 % (2584700)Peak memory usage: 12 MB
% 0.20/0.26 % (2584700)Instructions burned: 7 (million)
% 0.20/0.26 % (2584690)Success in time 0.017 s
% 0.20/0.26 % Vampire exiting
%------------------------------------------------------------------------------