%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO352^5 : 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 : n002.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 08:47:30 AM UTC 2026
% Result : Theorem 0.25s 0.37s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 22 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 82 ( 14 ~; 4 |; 4 &; 48 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 20 ( 0 ^; 19 !; 1 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
n: $i > $i ).
thf(func_def_1,type,
m: $i > $i ).
thf(func_def_5,type,
sK0: ( $i > $i ) > $o ).
thf(func_def_6,type,
vNOT: $o > $o ).
thf(func_def_8,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(f1,conjecture,
( ! [X1: $i > $o,X0: $i] :
( ( X1 @ ( m @ X0 ) )
=> ( X1 @ ( n @ X0 ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( X2 @ m )
=> ( X2 @ n ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cE5EXT) ).
thf(f2,negated_conjecture,
~ ( ! [X1: $i > $o,X0: $i] :
( ( X1 @ ( m @ X0 ) )
=> ( X1 @ ( n @ X0 ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( X2 @ m )
=> ( X2 @ n ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i > $o,X1: $i] :
( ( X0 @ ( m @ X1 ) )
=> ( X0 @ ( n @ X1 ) ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( X2 @ m )
=> ( X2 @ n ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X1: $i,X0: $i > $o] :
( ( $true
= ( X0 @ ( m @ X1 ) ) )
=> ( ( X0 @ ( n @ X1 ) )
= $true ) )
=> ! [X2: ( $i > $i ) > $o] :
( ( ( X2 @ m )
= $true )
=> ( ( X2 @ n )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( n @ X1 ) )
= $true )
| ( $true
!= ( X0 @ ( m @ X1 ) ) ) )
& ? [X2: ( $i > $i ) > $o] :
( ( ( X2 @ m )
= $true )
& ( ( X2 @ n )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( n @ X1 ) )
= $true )
| ( $true
!= ( X0 @ ( m @ X1 ) ) ) )
& ( ( sK0 @ m )
= $true )
& ( ( sK0 @ n )
!= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0)],[f5]) ).
thf(f7,plain,
( ( sK0 @ n )
!= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( ( sK0 @ m )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
!= ( X0 @ ( m @ X1 ) ) )
| ( ( X0 @ ( n @ X1 ) )
= $true ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f12,plain,
( ( $true != $true )
| ( m != n ) ),
inference(constrained_superposition,[],[f7,f8]) ).
thf(f13,plain,
m != n,
inference(trivial_inequality_removal,[],[f12]) ).
thf(f14,plain,
( ( n @ sK1 )
!= ( m @ sK1 ) ),
inference(negative_extensionality,[],[f13]) ).
thf(f16,plain,
! [X0: $i] :
( ( m @ X0 )
= ( n @ X0 ) ),
inference(leibniz_equality_elimination,[],[f9]) ).
thf(f34,plain,
( ( m @ sK1 )
!= ( m @ sK1 ) ),
inference(backward_demodulation,[],[f14,f16]) ).
thf(f35,plain,
$false,
inference(trivial_inequality_removal,[],[f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO352^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n002.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 16:50:52 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running higher-order theorem proving
% 0.25/0.33 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
% 0.25/0.37 % (1542330)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.37 % (1542340)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3807515810:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.25/0.37 % (1542340) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1542330-1542340"...
% 0.25/0.37 % (1542340)...printing done.
% 0.25/0.37 % (1542340)Refutation found. Thanks to Tanya!
% 0.25/0.37 % SZS status Theorem for theBenchmark
% 0.25/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.37 % (1542340)------------------------------
% 0.25/0.37 % (1542340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.37 % (1542340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.37 % (1542340)CaDiCaL version: 2.1.3
% 0.25/0.37 % (1542340)Termination reason: Refutation
% 0.25/0.37 % (1542340)Time elapsed: 0.002 s
% 0.25/0.37 % (1542340)Peak memory usage: 12 MB
% 0.25/0.37 % (1542340)Instructions burned: 2 (million)
% 0.25/0.37 % (1542330)Success in time 0.026 s
% 0.25/0.37 % Vampire exiting
%------------------------------------------------------------------------------