%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU697^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:30:49 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 13 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 106 ( 8 ~; 2 |; 2 &; 86 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 35 ( 14 ^; 18 !; 3 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_2,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_4,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
sK2: $i > $i ).
thf(f2,conjecture,
! [X1: $i,X0: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ( ( lam @ X0 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) )
= ( lam @ X0 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(f3,negated_conjecture,
~ ! [X1: $i,X0: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ( ( lam @ X0 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) )
= ( lam @ X0 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f6,plain,
~ ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( X2 @ X3 ) @ X0 ) )
=> ( ( lam @ X1 @ X0
@ ^ [X4: $i] : ( X2 @ X4 ) )
= ( lam @ X1 @ X0
@ ^ [X5: $i] : ( X2 @ X5 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X1: $i,X0: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( in @ ( X2 @ X3 ) @ X0 )
= $true ) )
=> ( ( lam @ X1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
= ( lam @ X1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ ( X2 @ X3 ) @ X0 )
= $true ) )
& ( ( lam @ X1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
!= ( lam @ X1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ! [X3: $i] :
( ( ( in @ X3 @ sK1 )
!= $true )
| ( ( in @ ( sK2 @ X3 ) @ sK0 )
= $true ) )
& ( ( lam @ sK1 @ sK0
@ ^ [Y0: $i] : ( sK2 @ Y0 ) )
!= ( lam @ sK1 @ sK0
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
thf(f11,plain,
( ( lam @ sK1 @ sK0
@ ^ [Y0: $i] : ( sK2 @ Y0 ) )
!= ( lam @ sK1 @ sK0
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
$false,
inference(trivial_inequality_removal,[],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU697^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n010.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:12:03 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.29 % (2915505)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (2915514)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3325449580:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.29 % (2915514) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2915505-2915514"...
% 0.23/0.29 % (2915514)...printing done.
% 0.23/0.29 % (2915514)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.29 % (2915514)------------------------------
% 0.23/0.29 % (2915514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (2915514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (2915514)CaDiCaL version: 2.1.3
% 0.23/0.29 % (2915514)Termination reason: Refutation
% 0.23/0.29 % (2915514)Time elapsed: 0.001 s
% 0.23/0.29 % (2915514)Peak memory usage: 11 MB
% 0.23/0.29 % (2915514)Instructions burned: 1 (million)
% 0.23/0.29 % (2915505)Success in time 0.032 s
% 0.23/0.29 % Vampire exiting
%------------------------------------------------------------------------------