%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO256^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 08:47:17 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 64 ( 16 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 102 ( 8 ~; 16 |; 0 &; 66 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 3 con; 0-4 aty)
% ( 9 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 42 ( 9 ^; 23 !; 10 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
vOR: $o > $o > $o ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_5,type,
sK0: a > $o ).
thf(func_def_6,type,
sK1: $o > $o ).
thf(func_def_7,type,
sK2: a > $o ).
thf(f1,conjecture,
! [X0: $o > $o,X2: a > $o,X1: a > $o] :
? [X3: $o] :
( ( X0 @ X3 )
<=> ( X0
@ ! [X4: a] :
( ( X1 @ X4 )
| ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM121) ).
thf(f2,negated_conjecture,
~ ! [X0: $o > $o,X2: a > $o,X1: a > $o] :
? [X3: $o] :
( ( X0 @ X3 )
<=> ( X0
@ ! [X4: a] :
( ( X1 @ X4 )
| ( X2 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $o > $o,X1: a > $o,X2: a > $o] :
? [X3: $o] :
( ( X0 @ X3 )
<=> ( X0
@ ! [X4: a] :
( ( X2 @ X4 )
| ( X1 @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X2: a > $o,X1: a > $o,X0: $o > $o] :
? [X3: $o] :
( ( X0 @ X3 )
= ( X0
@ ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X2: a > $o,X0: $o > $o,X1: a > $o] :
! [X3: $o] :
( ( X0 @ X3 )
!= ( X0
@ ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: $o > $o,X2: a > $o] :
! [X3: $o] :
( ( X1
@ ( !! @ a
@ ^ [Y0: a] :
( ( X2 @ Y0 )
| ( X0 @ Y0 ) ) ) )
!= ( X1 @ X3 ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
! [X3: $o] :
( ( sK1
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) ) )
!= ( sK1 @ X3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6]) ).
thf(f8,plain,
! [X3: $o] :
( ( sK1
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) ) )
!= ( sK1 @ X3 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X3: $o] :
( ( $true
= ( sK1
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) ) ) )
| ( $true
= ( sK1 @ X3 ) ) ),
inference(xor_proxy_clausification,[],[f8]) ).
thf(f11,plain,
! [X3: $o] :
( ( $false
= ( sK1 @ X3 ) )
| ( $false
= ( sK1
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) ) ) ) ),
inference(xor_proxy_clausification,[],[f8]) ).
thf(f12,plain,
( ( $true
= ( sK1
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) ) ) )
| ( $true != $true ) ),
inference(equality_factoring,[],[f10]) ).
thf(f14,plain,
( $true
= ( sK1
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f12]) ).
thf(f16,plain,
! [X3: $o] :
( ( $false
= ( sK1 @ X3 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f11,f14]) ).
thf(f17,plain,
! [X3: $o] :
( $false
= ( sK1 @ X3 ) ),
inference(trivial_inequality_removal,[],[f16]) ).
thf(f21,plain,
$true = $false,
inference(superposition,[],[f14,f17]) ).
thf(f24,plain,
$false,
inference(trivial_inequality_removal,[],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO256^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n005.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 16:41:31 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.26 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
% 0.23/0.31 % (1893862)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.31 % (1893871)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3584907611:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.31 % (1893871) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1893862-1893871"...
% 0.23/0.31 % (1893871)...printing done.
% 0.23/0.31 % (1893867)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2508975415:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.31 % (1893871)Refutation found. Thanks to Tanya!
% 0.23/0.31 % SZS status Theorem for theBenchmark
% 0.23/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.31 % (1893871)------------------------------
% 0.23/0.31 % (1893871)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (1893871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (1893871)CaDiCaL version: 2.1.3
% 0.23/0.31 % (1893871)Termination reason: Refutation
% 0.23/0.31 % (1893871)Time elapsed: 0.002 s
% 0.23/0.31 % (1893871)Peak memory usage: 12 MB
% 0.23/0.31 % (1893871)Instructions burned: 2 (million)
% 0.23/0.31 % (1893862)Success in time 0.041 s
% 0.23/0.31 % Vampire exiting
%------------------------------------------------------------------------------