%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL579^2 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:14:23 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 22 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 66 ( 11 ~; 4 |; 6 &; 33 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 14 ( 0 ^; 12 !; 2 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_5,type,
sK0: $i > $o ).
thf(func_def_6,type,
vNOT: $o > $o ).
thf(func_def_7,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ! [X0: $i > $o] :
( ( X0 @ cY )
=> ( X0 @ cX ) )
=> ! [X1: $i > $o] :
( ( X1 @ cX )
=> ( X1 @ cY ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM76A) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i > $o] :
( ( X0 @ cY )
=> ( X0 @ cX ) )
=> ! [X1: $i > $o] :
( ( X1 @ cX )
=> ( X1 @ cY ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i > $o] :
( ( X0 @ cY )
=> ( X0 @ cX ) )
=> ! [X1: $i > $o] :
( ( X1 @ cX )
=> ( X1 @ cY ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i > $o] :
( ( ( X0 @ cY )
= $true )
=> ( ( X0 @ cX )
= $true ) )
=> ! [X1: $i > $o] :
( ( ( X1 @ cX )
= $true )
=> ( ( X1 @ cY )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ? [X1: $i > $o] :
( ( ( X1 @ cY )
!= $true )
& ( ( X1 @ cX )
= $true ) )
& ! [X0: $i > $o] :
( ( ( X0 @ cY )
!= $true )
| ( ( X0 @ cX )
= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ? [X0: $i > $o] :
( ( ( X0 @ cY )
!= $true )
& ( ( X0 @ cX )
= $true ) )
& ! [X1: $i > $o] :
( ( ( X1 @ cY )
!= $true )
| ( ( X1 @ cX )
= $true ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ( sK0 @ cY )
!= $true )
& ( ( sK0 @ cX )
= $true )
& ! [X1: $i > $o] :
( ( ( X1 @ cY )
!= $true )
| ( ( X1 @ cX )
= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6]) ).
thf(f8,plain,
! [X1: $i > $o] :
( ( ( X1 @ cY )
!= $true )
| ( ( X1 @ cX )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( ( sK0 @ cX )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( ( sK0 @ cY )
!= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
cY = cX,
inference(leibniz_equality_elimination,[],[f8]) ).
thf(f29,plain,
( ( sK0 @ cY )
= $true ),
inference(constrained_superposition,[],[f9,f13]) ).
thf(f30,plain,
$false,
inference(forward_subsumption_resolution,[],[f29,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL579^2 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 09:00:50 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.20/0.27 % (975861)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (975867)lrs+10_16_si=on:nwc=1.5:random_seed=3461984761:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.27 % (975867) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-975861-975867"...
% 0.20/0.27 % (975867)...printing done.
% 0.20/0.27 % (975867)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (975867)------------------------------
% 0.20/0.27 % (975867)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (975867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (975867)CaDiCaL version: 2.1.3
% 0.20/0.27 % (975867)Termination reason: Refutation
% 0.20/0.27 % (975867)Time elapsed: 0.001 s
% 0.20/0.27 % (975867)Peak memory usage: 12 MB
% 0.20/0.27 % (975867)Instructions burned: 1 (million)
% 0.20/0.27 % (975861)Success in time 0.028 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------