%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV168^5 : 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 : n018.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 08:37:57 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 22 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 79 ( 7 ~; 0 |; 8 &; 60 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-4 aty)
% Number of variables : 75 ( 75 ^; 0 !; 0 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
q: ( a > a > a ) > a ).
thf(func_def_1,type,
p: ( a > a > a ) > a ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ( ( p
= ( ^ [X0: a > a > a] :
( X0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) ) ) )
& ( q
= ( ^ [X0: a > a > a] :
( X0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) ) ) ) )
=> ( p = q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM188_PARTIAL_pme) ).
thf(f2,negated_conjecture,
~ ( ( ( p
= ( ^ [X0: a > a > a] :
( X0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) ) ) )
& ( q
= ( ^ [X0: a > a > a] :
( X0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) ) ) ) )
=> ( p = q ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( p
= ( ^ [X0: a > a > a] :
( X0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X3: a,X4: a] : X4 ) ) ) )
& ( q
= ( ^ [X5: a > a > a] :
( X5
@ ( q
@ ^ [X6: a,X7: a] : X6 )
@ ( q
@ ^ [X8: a,X9: a] : X9 ) ) ) ) )
=> ( p = q ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( p
= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) )
& ( q
= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) ) )
=> ( q = p ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( q != p )
& ( p
= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) )
& ( q
= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( q != p )
& ( q
= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) )
& ( p
= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( p
= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( q
= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
q != p,
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
( q
!= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) ),
inference(definition_unfolding,[],[f9,f7]) ).
thf(f11,plain,
$false,
inference(forward_subsumption_resolution,[],[f10,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV168^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:20:27 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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
% 0.21/0.27 % (211465)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (211474)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3544652035:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.27 % (211474) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-211465-211474"...
% 0.21/0.27 % (211474)...printing done.
% 0.21/0.27 % (211474)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (211474)------------------------------
% 0.21/0.28 % (211474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (211474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (211474)CaDiCaL version: 2.1.3
% 0.21/0.28 % (211474)Termination reason: Refutation
% 0.21/0.28 % (211474)Time elapsed: 0.001 s
% 0.21/0.28 % (211474)Peak memory usage: 12 MB
% 0.21/0.28 % (211474)Instructions burned: 1 (million)
% 0.21/0.28 % (211465)Success in time 0.017 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------